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Biblioteca

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Theory of charges : a study of finitely additive measures / K. P. S. Bhaskara Rao, M. Bhaskara Rao
Theory of charges : a study of finitely additive measures / K. P. S. Bhaskara Rao, M. Bhaskara Rao
Autore Bhaskara Rao, K. P. S.
Pubbl/distr/stampa London : Academic press, 1983
Descrizione fisica 315 p. ; 23 cm.
Disciplina 515.42
Altri autori (Persone) Bhaskara Rao, M.
Collana Pure and applied mathematics. A series of monographs & textbooks [Academic Press], 0079-8169 ; 109
Soggetto topico Classical measure theory
Integration-research exposition
Measure-research exposition
ISBN 0120957809
Classificazione AMS 28-02
AMS 28-XX
AMS 28A
QA612
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNISALENTO-991001431339707536
Bhaskara Rao, K. P. S.  
London : Academic press, 1983
Materiale a stampa
Lo trovi qui: Univ. del Salento
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The theory of measures and integration [[electronic resource] /] / Eric M. Vestrup
The theory of measures and integration [[electronic resource] /] / Eric M. Vestrup
Autore Vestrup Eric M. <1971->
Pubbl/distr/stampa Hoboken, N.J., : Wiley-Interscience, c2003
Descrizione fisica 1 online resource (622 p.)
Disciplina 515.42
515/.42
Collana Wiley series in probability and statistics
Soggetto topico Measure theory
Integrals, Generalized
Soggetto genere / forma Electronic books.
ISBN 1-282-30745-2
9786612307454
0-470-31711-6
0-470-31795-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto THE THEORY OF MEASURES AND INTEGRATION; Contents; Preface; Acknowledgments; 1 Set Systems; 1.1 π-Systems, λ-Systems, and Semirings; 1.2 Fields; 1.3 σ--Fields; 1.4 The Borel σ-Field; 1.5 The k-Dimensional Borel σ-Field; 1.6 σ-Fields: Construction and Cardinality; 1.7 A Class of Ethereal Borel Sets; 2 Measures; 2.1 Measures; 2.2 Continuity of Measures; 2.3 A Class of Measures; 2.4 Appendix: Proof of the Stieltjes Theorem; 3 Extensions of Measures; 3.1 Extensions and Restrictions; 3.2 Outer Measures; 3.3 Caratheodory's Criterion; 3.4 Existence of Extensions
3.5 Uniqueness of Measures and Extensions3.6 The Completion Theorem; 3.7 The Relationship Between a(A) and M(μ*); 3.8 Approximations; 3.9 A Further Description of M(pμ); 3.10 A Correspondence Theorem; 4 Lebesgue Measure; 4.1 Lebesgue Measure: Existence and Uniqueness; 4.2 Lebesgue Sets; 4.3 Translation Invariance of Lebesgue Measure; 4.4 Linear Transformations; 4.5 The Existence of non-Lebesgue Sets; 4.6 The Cantor Set and the Lebesgue Function; 4.7 A Non-Bore1 Lebesgue Set; 4.8 The Impossibility Theorem; 4.9 Excursus: "Extremely Nonmeasurable Sets"; 5 Measurable Functions; 5.1 Measurability
5.2 Combining Measurable Functions5.3 Sequences of Measurable Functions; 5.4 Almost Everywhere; 5.5 Simple Functions; 5.6 Some Convergence Concepts; 5.7 Continuity and Measurability; 5.8 A Generalized Definition of Measurability; 6 The Lebesgue Integral; 6.1 Stage One: Simple Functions; 6.2 Stage Two: Nonnegative Functions; 6.3 Stage Three: General Measurable Functions; 6.4 Stage Four: Almost Everywhere Defined Functions; 7 Integrals Relative to Lebesgue Measure; 7.1 Semicontinuity; 7.2 Step Functions in Euclidean Space; 7.3 The Riemann Integral, Part One; 7.4 The Riemann Integral, Part Two
10.1 Product Measures10.2 The Fubini Theorems; 10.3 The Fubini Theorems in Euclidean Space; 10.4 The Generalized Minkowski Inequality; 10.5 Convolutions; 10.6 The Hard y-Littlewood Theorems; 11 Arbitrary Products of Measure Spaces; 1 1.1 Notation and Conventions; 1 1.2 Construction of the Product Measure; 1 1.3 Convergence Theorems in Product Space; 1 1.4 The L2 Strong Law; 1 1.5 Prelude to the L1 Strong Law; 1 1.6 The L1 Strong Law; References; Index
Record Nr. UNINA-9910144695103321
Vestrup Eric M. <1971->  
Hoboken, N.J., : Wiley-Interscience, c2003
Materiale a stampa
Lo trovi qui: Univ. Federico II
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The theory of measures and integration [[electronic resource] /] / Eric M. Vestrup
The theory of measures and integration [[electronic resource] /] / Eric M. Vestrup
Autore Vestrup Eric M. <1971->
Pubbl/distr/stampa Hoboken, N.J., : Wiley-Interscience, c2003
Descrizione fisica 1 online resource (622 p.)
Disciplina 515.42
515/.42
Collana Wiley series in probability and statistics
Soggetto topico Measure theory
Integrals, Generalized
ISBN 1-282-30745-2
9786612307454
0-470-31711-6
0-470-31795-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto THE THEORY OF MEASURES AND INTEGRATION; Contents; Preface; Acknowledgments; 1 Set Systems; 1.1 π-Systems, λ-Systems, and Semirings; 1.2 Fields; 1.3 σ--Fields; 1.4 The Borel σ-Field; 1.5 The k-Dimensional Borel σ-Field; 1.6 σ-Fields: Construction and Cardinality; 1.7 A Class of Ethereal Borel Sets; 2 Measures; 2.1 Measures; 2.2 Continuity of Measures; 2.3 A Class of Measures; 2.4 Appendix: Proof of the Stieltjes Theorem; 3 Extensions of Measures; 3.1 Extensions and Restrictions; 3.2 Outer Measures; 3.3 Caratheodory's Criterion; 3.4 Existence of Extensions
3.5 Uniqueness of Measures and Extensions3.6 The Completion Theorem; 3.7 The Relationship Between a(A) and M(μ*); 3.8 Approximations; 3.9 A Further Description of M(pμ); 3.10 A Correspondence Theorem; 4 Lebesgue Measure; 4.1 Lebesgue Measure: Existence and Uniqueness; 4.2 Lebesgue Sets; 4.3 Translation Invariance of Lebesgue Measure; 4.4 Linear Transformations; 4.5 The Existence of non-Lebesgue Sets; 4.6 The Cantor Set and the Lebesgue Function; 4.7 A Non-Bore1 Lebesgue Set; 4.8 The Impossibility Theorem; 4.9 Excursus: "Extremely Nonmeasurable Sets"; 5 Measurable Functions; 5.1 Measurability
5.2 Combining Measurable Functions5.3 Sequences of Measurable Functions; 5.4 Almost Everywhere; 5.5 Simple Functions; 5.6 Some Convergence Concepts; 5.7 Continuity and Measurability; 5.8 A Generalized Definition of Measurability; 6 The Lebesgue Integral; 6.1 Stage One: Simple Functions; 6.2 Stage Two: Nonnegative Functions; 6.3 Stage Three: General Measurable Functions; 6.4 Stage Four: Almost Everywhere Defined Functions; 7 Integrals Relative to Lebesgue Measure; 7.1 Semicontinuity; 7.2 Step Functions in Euclidean Space; 7.3 The Riemann Integral, Part One; 7.4 The Riemann Integral, Part Two
10.1 Product Measures10.2 The Fubini Theorems; 10.3 The Fubini Theorems in Euclidean Space; 10.4 The Generalized Minkowski Inequality; 10.5 Convolutions; 10.6 The Hard y-Littlewood Theorems; 11 Arbitrary Products of Measure Spaces; 1 1.1 Notation and Conventions; 1 1.2 Construction of the Product Measure; 1 1.3 Convergence Theorems in Product Space; 1 1.4 The L2 Strong Law; 1 1.5 Prelude to the L1 Strong Law; 1 1.6 The L1 Strong Law; References; Index
Record Nr. UNINA-9910830096603321
Vestrup Eric M. <1971->  
Hoboken, N.J., : Wiley-Interscience, c2003
Materiale a stampa
Lo trovi qui: Univ. Federico II
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A theory of semigroup valued measures / Maurice Sion
A theory of semigroup valued measures / Maurice Sion
Autore Sion, Maurice
Pubbl/distr/stampa Berlin : Springer-Verlag, 1973
Descrizione fisica 140 p. ; 24 cm
Disciplina 515.42
Collana Lecture notes in mathematics, 0075-8434 ; 355
Soggetto topico Lifting theory
Measure theory
Semigroups
Vector-valued measures
ISBN 3540065423
Classificazione AMS 28B10
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNISALENTO-991001437419707536
Sion, Maurice  
Berlin : Springer-Verlag, 1973
Materiale a stampa
Lo trovi qui: Univ. del Salento
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Theory of the integral / S. Saks ; english translation by L. C. Young with two additional notes by S. Banach
Theory of the integral / S. Saks ; english translation by L. C. Young with two additional notes by S. Banach
Autore Saks, Stanislaw
Edizione [2. rev. ed.]
Pubbl/distr/stampa New York : Dover Publications Inc., 1964
Descrizione fisica XV, 343 p. ; 22 cm
Disciplina 515.42
Collana Dover books on advanced mathematics
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNINA-990000848250403321
Saks, Stanislaw  
New York : Dover Publications Inc., 1964
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Thermodynamic formalism : CIRM Jean-Morlet Chair, Fall 2019 / / Mark Pollicott, Sandro Vaienti, editors
Thermodynamic formalism : CIRM Jean-Morlet Chair, Fall 2019 / / Mark Pollicott, Sandro Vaienti, editors
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2021]
Descrizione fisica 1 online resource (534 pages)
Disciplina 515.42
Collana Lecture notes in mathematics (Springer-Verlag)
Soggetto topico Ergodic theory
Teoria ergòdica
Fractals
Termodinàmica
Soggetto genere / forma Llibres electrònics
ISBN 3-030-74863-4
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Foreword -- Preface -- Contents -- Contributors -- Part I Specifications and Expansiveness -- 1 Beyond Bowen's Specification Property -- 1.1 Introduction -- 1.2 Main Ideas: Uniqueness of the Measure of Maximal Entropy -- 1.2.1 Entropy and Thermodynamic Formalism -- 1.2.2 Bowen's Original Argument: The Symbolic Case -- 1.2.2.1 The Specification Property in a Shift Space -- 1.2.2.2 The Lower Gibbs Bound as the Mechanism for Uniqueness -- 1.2.2.3 Building a Gibbs Measure -- 1.2.3 Relaxing Specification: Decompositions of the Language -- 1.2.3.1 Decompositions -- 1.2.3.2 An Example: Beta Shifts -- 1.2.3.3 Periodic Points -- 1.2.4 Beyond Shift Spaces: Expansivity in Bowen's Argument -- 1.2.4.1 Topological Entropy -- 1.2.4.2 Expansivity -- 1.2.4.3 Specification -- 1.2.4.4 Bowen's Proof Revisited -- 1.3 Non-uniform Bowen Hypotheses and Equilibrium States -- 1.3.1 Relaxing the Expansivity Hypothesis -- 1.3.2 Derived-from-Anosov Systems -- 1.3.2.1 Construction of the Mañé Example -- 1.3.2.2 Estimating the Entropy of Obstructions -- 1.3.2.3 Specification for Mañé Examples -- 1.3.3 The General Result for MMEs in Discrete-Time -- 1.3.4 Partially Hyperbolic Systems with One-Dimensional Center -- 1.3.4.1 A Small Collection of Obstructions -- 1.3.4.2 A Good Collection with Specification -- 1.3.5 Unique Equilibrium States -- 1.3.5.1 Topological Pressure -- 1.3.5.2 Regularity of the Potential Function: The Bowen Property -- 1.3.5.3 The Most General Discrete-Time Result -- 1.3.5.4 Partial Hyperbolicity -- 1.4 Geodesic Flows -- 1.4.1 Geometric Preliminaries -- 1.4.1.1 Overview -- 1.4.1.2 Surfaces -- 1.4.1.3 Invariant Foliations via Horospheres -- 1.4.1.4 Jacobi Fields and Local Construction of Stables/Unstables -- 1.4.2 Equilibrium States for Geodesic Flows -- 1.4.2.1 The General Uniqueness Result for Flows.
1.4.2.2 Geodesic Flows in Non-positive Curvature -- 1.4.2.3 Uniqueness Can Fail Without a Pressure Gap -- 1.4.2.4 Uniqueness Given a Pressure Gap -- 1.4.2.5 Pressure and Periodic Orbits -- 1.4.2.6 Main Ideas of the Proof of Uniqueness -- 1.4.2.7 Unique MMEs for Surfaces Without Conjugate Points -- 1.4.2.8 Geodesic Flows on Metric Spaces -- 1.4.3 Kolmogorov Property for Equilibrium States -- 1.4.3.1 Moving Up the Mixing Hierarchy -- 1.4.3.2 Ledrappier's Approach -- 1.4.3.3 Decompositions for Products -- 1.4.3.4 Expansivity Issues -- 1.4.4 Knieper's Entropy Gap -- 1.4.4.1 Entropy in the Singular Set -- 1.4.4.2 Warm-Up: Shifts with Specification -- 1.4.4.3 Entropy Gap for Geodesic Flow -- 1.4.4.4 Other Applications of Pressure Production -- References -- 2 The Role of Continuity and Expansiveness on Leo and Periodic Specification Properties -- 2.1 Introduction -- 2.2 Definitions -- 2.3 Proofs -- 2.3.1 Proof of Theorem 1.2 -- 2.3.2 Proof of Theorem 1.3 -- 2.3.3 Proof of Theorem 1.4 -- 2.4 Examples -- References -- Part II Low Dimensional Dynamics and Thermodynamics Formalism -- 3 Thermodynamic Formalism and Geometric Applications for Transcendental Meromorphic and Entire Functions -- 3.1 Introduction -- 3.2 Notation -- 3.3 Transcendental Functions, Hyperbolicity and Expansion -- 3.3.1 Dynamical Preliminaries -- 3.3.2 Hyperbolicity and Expansion -- 3.3.3 Disjoint Type Entire Functions -- 3.4 Topological Pressure and Conformal Measures -- 3.4.1 Topological Pressure -- 3.4.2 Conformal Measures and Transfer Operator -- 3.4.3 Existence of Conformal Measures -- 3.4.4 Conformal Measures on the Radial Set and Recurrence -- 3.4.5 2-Conformal Measures -- 3.5 Perron-Frobenus-Ruelle Theorem, Spectral Gap and Applications -- 3.5.1 Growth Conditions -- 3.5.2 Geometry of Tracts -- 3.5.2.1 Hölder Tracts -- 3.5.2.2 Negative Spectrum.
3.5.2.3 Back to the Thermodynamic Formalism and Its Applications -- 3.6 Hyperbolic Dimension and Bowen's Formula -- 3.6.1 Estimates for the Hyperbolic Dimension -- 3.6.2 Bowen's Formula -- 3.7 Real Analyticity of Fractal Dimensions -- 3.8 Beyond Hyperbolicity -- References -- Part III Probability Theory Ergodicity and Thermodynamic Formalism -- 4 Recurrent Sets for Ergodic Sums of an Integer Valued Function -- 4.1 Introduction -- 4.2 Non Centered Case for d = 1 -- 4.2.1 Preliminaries -- 4.2.1.1 Special Map Tf -- 4.2.1.2 Aperiodicity -- 4.2.1.3 From μ(f) > -- 0 to f ≥1 -- 4.2.2 Sequence of Positive Density -- 4.2.3 Arithmetic Sequences -- 4.2.4 Arbitrary Sequences and Mixing Special Flows -- 4.2.5 Intersection of Cocycles -- 4.2.5.1 Return Times Theorem -- 4.2.6 Cocycles for T and T-1 -- 4.3 Centered Case, d ≥1 -- 4.3.1 Values of a Regular Cocycle -- 4.3.2 Hyperbolic Models -- 4.3.3 A Cocycle Disjoint from a Sequence with Unbounded Gaps (UGB) -- 4.4 Recurrent Sets for Random Walks -- References -- 5 Almost Sure Invariance Principle for Random Distance Expanding Maps with a Nonuniform Decay of Correlations -- 5.1 Introduction -- 5.2 Random Distance Expanding Maps -- 5.2.1 Transfer Operators -- 5.3 A Refined Version of Gouëzel's Theorem -- 5.4 Main Result -- References -- 6 Limit Theorem for Reflected Random Walks -- 6.1 Introduction and Notations -- 6.2 Fluctuations of Random Walks and Auxiliary Estimates -- 6.2.1 On the Fluctuation of Random Walks -- 6.2.2 Conditional Limit Theorems -- 6.3 On the Sub-process of Reflections -- 6.3.1 On the Spectrum of the Transition Probabilities Matrix R -- 6.3.2 A Renewal Limit Theorem for the Times of Reflections -- 6.4 Proof of Theorem 6.1.1 -- 6.4.1 One-Dimensional Distribution -- 6.4.2 Two-Dimensional Distributions -- 6.4.2.1 Estimate of A1(n) -- 6.4.2.2 Estimate of A2 (n) -- 6.4.2.3 Conclusion.
6.4.3 Finite Dimensional Distributions -- 6.4.4 Tightness -- 6.5 Auxiliary Proofs -- References -- 7 The Strong Borel-Cantelli Property in Conventional and Nonconventional Setups -- 7.1 Introduction -- 7.2 Preliminaries and Main Results -- 7.3 Proof of Theorem 7.2.2 -- 7.3.1 The Case =1 -- 7.3.2 The Case > -- 1 -- 7.4 Proof of Theorem 7.2.3(i) -- 7.5 Proof of Theorem 7.2.3(ii) -- 7.6 Asymptotics of Maximums of Logarithmic Distance Functions -- 7.7 Asymptotics of Hitting Times -- References -- 8 Application of the Convergence of the Spatio-Temporal Processes for Visits to Small Sets -- 8.1 Introduction -- 8.2 Convergence Results for Transformations and Special Flows -- 8.3 Number of Visits to a Small Set Before the First Visit to a Second Small Set -- 8.4 Number of High Records -- 8.5 Line Process of Random Geodesics -- 8.6 Time Spent by a Flow in a Small Set -- Appendix: Visits by the Sinai Flow to a Finite Union of Balls in the Billiard Domain -- References -- Part IV Geometry and Thermodynamics Formation -- 9 Rate of Mixing for Equilibrium States in Negative Curvature and Trees -- 9.1 A Patterson-Sullivan Construction of Equilibrium States -- 9.2 Basic Ergodic Properties of Gibbs Measures -- 9.2.1 The Gibbs Property -- 9.2.2 Ergodicity -- 9.2.3 Mixing -- 9.3 Coding and Rate of Mixing for Geodesic Flows on Trees -- 9.3.1 Coding -- 9.3.2 Variational Principle for Simplicial Trees -- 9.3.3 Rate of Mixing for Simplicial Trees -- References -- 10 Statistical Properties of the Rauzy-Veech-Zorich Map -- 10.1 Introduction -- 10.2 Interval Exchange Transformation -- 10.2.1 The Rauzy Class of Permutations -- 10.2.2 The Rauzy-Veech Renormalization T0 -- 10.2.3 The Zorich Accelerated Renormalization T1 -- 10.2.4 The Induced Map T2 on a Smaller Set -- 10.3 Transfer Operators -- 10.4 Statistical Properties for T2.
10.4.1 The Central Limit Theorem and Functional Central Limit Theorem -- 10.4.2 Almost Sure Invariance Principles -- 10.5 Statistical Properties for T1 -- 10.6 Transfer Operators and Analytic Functions -- 10.7 Zeta Functions and Lyapunov Exponents -- 10.8 A Glimpse into Teichmüller Flows -- 10.9 Comments on Pressure -- References -- 11 Entropy Rigidity, Pressure Metric, and Immersed Surfaces in Hyperbolic 3-Manifolds -- 11.1 Introduction -- 11.1.1 Outline of the Paper -- 11.2 Background from the Thermodynamic Formalism -- 11.2.1 Flows and Reparametrization -- 11.2.2 Periods and Measures -- 11.2.3 Entropy, Pressure, and Equilibrium States -- 11.2.4 Anosov Flows -- 11.2.5 A Livšic Type Theorem -- 11.2.6 Variance and Derivatives of the Pressure -- 11.2.7 The Pressure Metric -- 11.3 Background from Geometry -- 11.3.1 δ-Hyperbolic Spaces -- 11.3.2 Quasi-Isometries -- 11.3.3 Negatively Curved Manifolds and the Group of Isometries -- 11.3.4 Hölder Cocycles -- 11.3.5 Immersed Surfaces in Hyperbolic 3-Manifolds -- 11.3.6 Minimal Hyperbolic Germs -- 11.4 Immersed and Embedded Surfaces in Hyperbolic 3-Manifolds -- 11.4.1 Immersed Minimal Surfaces -- 11.4.2 Embedded Surfaces in Hyperbolic 3-Manifolds -- 11.4.3 The Manhattan Curve for Immersed Surfaces -- 11.5 Minimal Hyperbolic Germs -- 11.5.1 Quasifuchsian Spaces -- 11.5.2 Manhattan Curve for Almost-Fuchsian Space -- 11.5.3 Metrics on F -- References -- 12 Higher Teichmüller Theory for Surface Groups and Shifts of Finite Type -- 12.1 Introduction -- 12.2 Representations and Proximality -- 12.3 Symbolic Dynamics -- 12.4 Thermodynamic Formalism -- 12.5 Analyticity of the Metric and the Entropy -- 12.6 Proof of Theorem 12.4 -- References -- Part V Fractal Geometry -- 13 Dimension Estimates for C1 Iterated Function Systems and C1 Repellers, a Survey -- 13.1 Introduction -- 13.2 Notation.
13.2.1 Definitions of Fractal Dimensions of Sets and Measures.
Record Nr. UNINA-9910502654503321
Cham, Switzerland : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Thermodynamic formalism : CIRM Jean-Morlet Chair, Fall 2019 / / Mark Pollicott, Sandro Vaienti, editors
Thermodynamic formalism : CIRM Jean-Morlet Chair, Fall 2019 / / Mark Pollicott, Sandro Vaienti, editors
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2021]
Descrizione fisica 1 online resource (534 pages)
Disciplina 515.42
Collana Lecture notes in mathematics (Springer-Verlag)
Soggetto topico Ergodic theory
Teoria ergòdica
Fractals
Termodinàmica
Soggetto genere / forma Llibres electrònics
ISBN 3-030-74863-4
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Foreword -- Preface -- Contents -- Contributors -- Part I Specifications and Expansiveness -- 1 Beyond Bowen's Specification Property -- 1.1 Introduction -- 1.2 Main Ideas: Uniqueness of the Measure of Maximal Entropy -- 1.2.1 Entropy and Thermodynamic Formalism -- 1.2.2 Bowen's Original Argument: The Symbolic Case -- 1.2.2.1 The Specification Property in a Shift Space -- 1.2.2.2 The Lower Gibbs Bound as the Mechanism for Uniqueness -- 1.2.2.3 Building a Gibbs Measure -- 1.2.3 Relaxing Specification: Decompositions of the Language -- 1.2.3.1 Decompositions -- 1.2.3.2 An Example: Beta Shifts -- 1.2.3.3 Periodic Points -- 1.2.4 Beyond Shift Spaces: Expansivity in Bowen's Argument -- 1.2.4.1 Topological Entropy -- 1.2.4.2 Expansivity -- 1.2.4.3 Specification -- 1.2.4.4 Bowen's Proof Revisited -- 1.3 Non-uniform Bowen Hypotheses and Equilibrium States -- 1.3.1 Relaxing the Expansivity Hypothesis -- 1.3.2 Derived-from-Anosov Systems -- 1.3.2.1 Construction of the Mañé Example -- 1.3.2.2 Estimating the Entropy of Obstructions -- 1.3.2.3 Specification for Mañé Examples -- 1.3.3 The General Result for MMEs in Discrete-Time -- 1.3.4 Partially Hyperbolic Systems with One-Dimensional Center -- 1.3.4.1 A Small Collection of Obstructions -- 1.3.4.2 A Good Collection with Specification -- 1.3.5 Unique Equilibrium States -- 1.3.5.1 Topological Pressure -- 1.3.5.2 Regularity of the Potential Function: The Bowen Property -- 1.3.5.3 The Most General Discrete-Time Result -- 1.3.5.4 Partial Hyperbolicity -- 1.4 Geodesic Flows -- 1.4.1 Geometric Preliminaries -- 1.4.1.1 Overview -- 1.4.1.2 Surfaces -- 1.4.1.3 Invariant Foliations via Horospheres -- 1.4.1.4 Jacobi Fields and Local Construction of Stables/Unstables -- 1.4.2 Equilibrium States for Geodesic Flows -- 1.4.2.1 The General Uniqueness Result for Flows.
1.4.2.2 Geodesic Flows in Non-positive Curvature -- 1.4.2.3 Uniqueness Can Fail Without a Pressure Gap -- 1.4.2.4 Uniqueness Given a Pressure Gap -- 1.4.2.5 Pressure and Periodic Orbits -- 1.4.2.6 Main Ideas of the Proof of Uniqueness -- 1.4.2.7 Unique MMEs for Surfaces Without Conjugate Points -- 1.4.2.8 Geodesic Flows on Metric Spaces -- 1.4.3 Kolmogorov Property for Equilibrium States -- 1.4.3.1 Moving Up the Mixing Hierarchy -- 1.4.3.2 Ledrappier's Approach -- 1.4.3.3 Decompositions for Products -- 1.4.3.4 Expansivity Issues -- 1.4.4 Knieper's Entropy Gap -- 1.4.4.1 Entropy in the Singular Set -- 1.4.4.2 Warm-Up: Shifts with Specification -- 1.4.4.3 Entropy Gap for Geodesic Flow -- 1.4.4.4 Other Applications of Pressure Production -- References -- 2 The Role of Continuity and Expansiveness on Leo and Periodic Specification Properties -- 2.1 Introduction -- 2.2 Definitions -- 2.3 Proofs -- 2.3.1 Proof of Theorem 1.2 -- 2.3.2 Proof of Theorem 1.3 -- 2.3.3 Proof of Theorem 1.4 -- 2.4 Examples -- References -- Part II Low Dimensional Dynamics and Thermodynamics Formalism -- 3 Thermodynamic Formalism and Geometric Applications for Transcendental Meromorphic and Entire Functions -- 3.1 Introduction -- 3.2 Notation -- 3.3 Transcendental Functions, Hyperbolicity and Expansion -- 3.3.1 Dynamical Preliminaries -- 3.3.2 Hyperbolicity and Expansion -- 3.3.3 Disjoint Type Entire Functions -- 3.4 Topological Pressure and Conformal Measures -- 3.4.1 Topological Pressure -- 3.4.2 Conformal Measures and Transfer Operator -- 3.4.3 Existence of Conformal Measures -- 3.4.4 Conformal Measures on the Radial Set and Recurrence -- 3.4.5 2-Conformal Measures -- 3.5 Perron-Frobenus-Ruelle Theorem, Spectral Gap and Applications -- 3.5.1 Growth Conditions -- 3.5.2 Geometry of Tracts -- 3.5.2.1 Hölder Tracts -- 3.5.2.2 Negative Spectrum.
3.5.2.3 Back to the Thermodynamic Formalism and Its Applications -- 3.6 Hyperbolic Dimension and Bowen's Formula -- 3.6.1 Estimates for the Hyperbolic Dimension -- 3.6.2 Bowen's Formula -- 3.7 Real Analyticity of Fractal Dimensions -- 3.8 Beyond Hyperbolicity -- References -- Part III Probability Theory Ergodicity and Thermodynamic Formalism -- 4 Recurrent Sets for Ergodic Sums of an Integer Valued Function -- 4.1 Introduction -- 4.2 Non Centered Case for d = 1 -- 4.2.1 Preliminaries -- 4.2.1.1 Special Map Tf -- 4.2.1.2 Aperiodicity -- 4.2.1.3 From μ(f) > -- 0 to f ≥1 -- 4.2.2 Sequence of Positive Density -- 4.2.3 Arithmetic Sequences -- 4.2.4 Arbitrary Sequences and Mixing Special Flows -- 4.2.5 Intersection of Cocycles -- 4.2.5.1 Return Times Theorem -- 4.2.6 Cocycles for T and T-1 -- 4.3 Centered Case, d ≥1 -- 4.3.1 Values of a Regular Cocycle -- 4.3.2 Hyperbolic Models -- 4.3.3 A Cocycle Disjoint from a Sequence with Unbounded Gaps (UGB) -- 4.4 Recurrent Sets for Random Walks -- References -- 5 Almost Sure Invariance Principle for Random Distance Expanding Maps with a Nonuniform Decay of Correlations -- 5.1 Introduction -- 5.2 Random Distance Expanding Maps -- 5.2.1 Transfer Operators -- 5.3 A Refined Version of Gouëzel's Theorem -- 5.4 Main Result -- References -- 6 Limit Theorem for Reflected Random Walks -- 6.1 Introduction and Notations -- 6.2 Fluctuations of Random Walks and Auxiliary Estimates -- 6.2.1 On the Fluctuation of Random Walks -- 6.2.2 Conditional Limit Theorems -- 6.3 On the Sub-process of Reflections -- 6.3.1 On the Spectrum of the Transition Probabilities Matrix R -- 6.3.2 A Renewal Limit Theorem for the Times of Reflections -- 6.4 Proof of Theorem 6.1.1 -- 6.4.1 One-Dimensional Distribution -- 6.4.2 Two-Dimensional Distributions -- 6.4.2.1 Estimate of A1(n) -- 6.4.2.2 Estimate of A2 (n) -- 6.4.2.3 Conclusion.
6.4.3 Finite Dimensional Distributions -- 6.4.4 Tightness -- 6.5 Auxiliary Proofs -- References -- 7 The Strong Borel-Cantelli Property in Conventional and Nonconventional Setups -- 7.1 Introduction -- 7.2 Preliminaries and Main Results -- 7.3 Proof of Theorem 7.2.2 -- 7.3.1 The Case =1 -- 7.3.2 The Case > -- 1 -- 7.4 Proof of Theorem 7.2.3(i) -- 7.5 Proof of Theorem 7.2.3(ii) -- 7.6 Asymptotics of Maximums of Logarithmic Distance Functions -- 7.7 Asymptotics of Hitting Times -- References -- 8 Application of the Convergence of the Spatio-Temporal Processes for Visits to Small Sets -- 8.1 Introduction -- 8.2 Convergence Results for Transformations and Special Flows -- 8.3 Number of Visits to a Small Set Before the First Visit to a Second Small Set -- 8.4 Number of High Records -- 8.5 Line Process of Random Geodesics -- 8.6 Time Spent by a Flow in a Small Set -- Appendix: Visits by the Sinai Flow to a Finite Union of Balls in the Billiard Domain -- References -- Part IV Geometry and Thermodynamics Formation -- 9 Rate of Mixing for Equilibrium States in Negative Curvature and Trees -- 9.1 A Patterson-Sullivan Construction of Equilibrium States -- 9.2 Basic Ergodic Properties of Gibbs Measures -- 9.2.1 The Gibbs Property -- 9.2.2 Ergodicity -- 9.2.3 Mixing -- 9.3 Coding and Rate of Mixing for Geodesic Flows on Trees -- 9.3.1 Coding -- 9.3.2 Variational Principle for Simplicial Trees -- 9.3.3 Rate of Mixing for Simplicial Trees -- References -- 10 Statistical Properties of the Rauzy-Veech-Zorich Map -- 10.1 Introduction -- 10.2 Interval Exchange Transformation -- 10.2.1 The Rauzy Class of Permutations -- 10.2.2 The Rauzy-Veech Renormalization T0 -- 10.2.3 The Zorich Accelerated Renormalization T1 -- 10.2.4 The Induced Map T2 on a Smaller Set -- 10.3 Transfer Operators -- 10.4 Statistical Properties for T2.
10.4.1 The Central Limit Theorem and Functional Central Limit Theorem -- 10.4.2 Almost Sure Invariance Principles -- 10.5 Statistical Properties for T1 -- 10.6 Transfer Operators and Analytic Functions -- 10.7 Zeta Functions and Lyapunov Exponents -- 10.8 A Glimpse into Teichmüller Flows -- 10.9 Comments on Pressure -- References -- 11 Entropy Rigidity, Pressure Metric, and Immersed Surfaces in Hyperbolic 3-Manifolds -- 11.1 Introduction -- 11.1.1 Outline of the Paper -- 11.2 Background from the Thermodynamic Formalism -- 11.2.1 Flows and Reparametrization -- 11.2.2 Periods and Measures -- 11.2.3 Entropy, Pressure, and Equilibrium States -- 11.2.4 Anosov Flows -- 11.2.5 A Livšic Type Theorem -- 11.2.6 Variance and Derivatives of the Pressure -- 11.2.7 The Pressure Metric -- 11.3 Background from Geometry -- 11.3.1 δ-Hyperbolic Spaces -- 11.3.2 Quasi-Isometries -- 11.3.3 Negatively Curved Manifolds and the Group of Isometries -- 11.3.4 Hölder Cocycles -- 11.3.5 Immersed Surfaces in Hyperbolic 3-Manifolds -- 11.3.6 Minimal Hyperbolic Germs -- 11.4 Immersed and Embedded Surfaces in Hyperbolic 3-Manifolds -- 11.4.1 Immersed Minimal Surfaces -- 11.4.2 Embedded Surfaces in Hyperbolic 3-Manifolds -- 11.4.3 The Manhattan Curve for Immersed Surfaces -- 11.5 Minimal Hyperbolic Germs -- 11.5.1 Quasifuchsian Spaces -- 11.5.2 Manhattan Curve for Almost-Fuchsian Space -- 11.5.3 Metrics on F -- References -- 12 Higher Teichmüller Theory for Surface Groups and Shifts of Finite Type -- 12.1 Introduction -- 12.2 Representations and Proximality -- 12.3 Symbolic Dynamics -- 12.4 Thermodynamic Formalism -- 12.5 Analyticity of the Metric and the Entropy -- 12.6 Proof of Theorem 12.4 -- References -- Part V Fractal Geometry -- 13 Dimension Estimates for C1 Iterated Function Systems and C1 Repellers, a Survey -- 13.1 Introduction -- 13.2 Notation.
13.2.1 Definitions of Fractal Dimensions of Sets and Measures.
Record Nr. UNISA-996466405503316
Cham, Switzerland : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
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Thomas Jefferson and his Decimals 1775–1810: Neglected Years in the History of U.S. School Mathematics / / by M.A. (Ken) Clements, Nerida F. Ellerton
Thomas Jefferson and his Decimals 1775–1810: Neglected Years in the History of U.S. School Mathematics / / by M.A. (Ken) Clements, Nerida F. Ellerton
Autore Clements M.A. (Ken)
Edizione [1st ed. 2015.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015
Descrizione fisica 1 online resource (219 p.)
Disciplina 370
515.42
Soggetto topico Mathematics—Study and teaching 
Measure theory
Mathematics Education
Measure and Integration
ISBN 3-319-02505-8
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Early Moves Toward Metrication in Europe -- Measurement Chaos in North America, 1780–1980 -- Opportunity Lost: Big Money Successfully Thwarts Thomas Jefferson’s Push for Metrication 1776–1793 -- Muddling Along: Opposition to Moves for Metrication, 1793–1920 -- David Eugene Smith’s Involvement in the Metrication Issue, 1920–1935 -- The Decision for Metrication, 1970 -- Reaganomics, Big Money, and the Crushing of the Metric Dream, 1970-1980 -- Why has the United States Never Achieved Metrication?.
Record Nr. UNINA-9910484867203321
Clements M.A. (Ken)  
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015
Materiale a stampa
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Topics in ergodic theory / William Parry
Topics in ergodic theory / William Parry
Autore PARRY, William
Pubbl/distr/stampa Cambridge : University Press, copyr. 1981
Descrizione fisica X, 110 p. : ill. ; 21 cm
Disciplina 515.42
Collana Cambridge tracts in mathematics
Soggetto topico Teoria ergodica
ISBN 0-521-22986-3
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNISA-990003230920203316
PARRY, William  
Cambridge : University Press, copyr. 1981
Materiale a stampa
Lo trovi qui: Univ. di Salerno
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Topics in ergodic theory / William Parry
Topics in ergodic theory / William Parry
Autore Parry, William
Pubbl/distr/stampa Cambridge : Cambridge University Press, 1981
Descrizione fisica x, 110 p. ; 22 cm
Disciplina 515.42
Collana Cambridge tracts in mathematics
Soggetto non controllato Teoria ergotica
ISBN 0-521-22986-3
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNINA-990003763060403321
Parry, William  
Cambridge : Cambridge University Press, 1981
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui