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Henstock-Kurzweil integration on euclidean spaces [[electronic resource] /] / Lee Tuo Yeong
| Henstock-Kurzweil integration on euclidean spaces [[electronic resource] /] / Lee Tuo Yeong |
| Autore | Lee Tuo Yeong <1967-> |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, N.J., : World Scientific, c2011 |
| Descrizione fisica | 1 online resource (325 p.) |
| Disciplina | 515.43 |
| Collana | Series in real analysis |
| Soggetto topico |
Henstock-Kurzweil integral
Lebesgue integral Calculus, Integral |
| ISBN |
1-283-23477-7
9786613234773 981-4324-59-0 |
| Classificazione |
SK 430
SK 620 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; 1. The one-dimensional Henstock-Kurzweil integral; 1.1 Introduction and Cousin's Lemma; 1.2 Definition of the Henstock-Kurzweil integral; 1.3 Simple properties; 1.4 Saks-Henstock Lemma; 1.5 Notes and Remarks; 2. The multiple Henstock-Kurzweil integral; 2.1 Preliminaries; 2.2 The Henstock-Kurzweil integral; 2.3 Simple properties; 2.4 Saks-Henstock Lemma; 2.5 Fubini's Theorem; 2.6 Notes and Remarks; 3. Lebesgue integrable functions; 3.1 Introduction; 3.2 Some convergence theorems for Lebesgue integrals; 3.3 μm-measurable sets; 3.4 A characterization of μm-measurable sets
3.5 μm-measurable functions3.6 Vitali Covering Theorem; 3.7 Further properties of Lebesgue integrable functions; 3.8 The Lp spaces; 3.9 Lebesgue's criterion for Riemann integrability; 3.10 Some characterizations of Lebesgue integrable functions; 3.11 Some results concerning one-dimensional Lebesgue integral; 3.12 Notes and Remarks; 4. Further properties of Henstock-Kurzweil integrable functions; 4.1 A necessary condition for Henstock-Kurzweil integrability; 4.2 A result of Kurzweil and Jarn ́ık; 4.3 Some necessary and su cient conditions for Henstock- Kurzweil integrability 4.4 Harnack extension for one-dimensional Henstock-Kurzweil integrals4.5 Other results concerning one-dimensional Henstock- Kurzweil integral; 4.6 Notes and Remarks; 5. The Henstock variational measure; 5.1 Lebesgue outer measure; 5.2 Basic properties of the Henstock variational measure; 5.3 Another characterization of Lebesgue integrable functions; 5.4 A result of Kurzweil and Jarn ́ık revisited; 5.5 A measure-theoretic characterization of the Henstock- Kurzweil integral; 5.6 Product variational measures; 5.7 Notes and Remarks; 6. Multipliers for the Henstock-Kurzweil integral 6.1 One-dimensional integration by parts6.2 On functions of bounded variation in the sense of Vitali; 6.3 The m-dimensional Riemann-Stieltjes integral; 6.4 A multiple integration by parts for the Henstock-Kurzweil integral; 6.5 Kurzweil's multiple integration by parts formula for the Henstock-Kurzweil integral; 6.6 Riesz Representation Theorems; 6.7 Characterization of multipliers for the Henstock-Kurzweil integral; 6.8 A Banach-Steinhaus Theorem for the space of Henstock- Kurzweil integrable functions; 6.9 Notes and Remarks; 7. Some selected topics in trigonometric series 7.1 A generalized Dirichlet test7.2 Fourier series; 7.3 Some examples of Fourier series; 7.4 Some Lebesgue integrability theorems for trigonometric series; 7.5 Boas' results; 7.6 On a result of Hardy and Littlewood concerning Fourier series; 7.7 Notes and Remarks; 8. Some applications of the Henstock-Kurzweil integral to double trigonometric series; 8.1 Regularly convergent double series; 8.2 Double Fourier series; 8.3 Some examples of double Fourier series; 8.4 A Lebesgue integrability theorem for double cosine series; 8.5 A Lebesgue integrability theorem for double sine series 8.6 A convergence theorem for Henstock-Kurzweil integrals |
| Record Nr. | UNINA-9910788961403321 |
Lee Tuo Yeong <1967->
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| Singapore ; ; Hackensack, N.J., : World Scientific, c2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Measure and integration theory [[electronic resource] /] / Heinz Bauer ; translated from the German by Robert B. Burckel
| Measure and integration theory [[electronic resource] /] / Heinz Bauer ; translated from the German by Robert B. Burckel |
| Autore | Bauer Heinz <1928-> |
| Pubbl/distr/stampa | Berlin ; ; New York, : W. de Gruyter, 2001 |
| Descrizione fisica | 1 online resource (248 p.) |
| Disciplina | 530.8/01 |
| Altri autori (Persone) | BurckelRobert B |
| Collana | De Gruyter studies in mathematics |
| Soggetto topico |
Measure theory
Integrals, Generalized |
| ISBN | 3-11-086620-X |
| Classificazione | SK 430 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Chapter I Measure Theory -- Chapter II Integration Theory -- Chapter III Product Measures -- Chapter IV Measures on Topological Spaces -- Bibliography -- Symbol Index -- Name Index -- Subject Index -- Back matter |
| Record Nr. | UNINA-9910785835203321 |
|
Bauer Heinz <1928->
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||
| Berlin ; ; New York, : W. de Gruyter, 2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Selecta / / Heinz Bauer ; edited by Herbert Heyer, Niels Jacob, Ivan Netuka
| Selecta / / Heinz Bauer ; edited by Herbert Heyer, Niels Jacob, Ivan Netuka |
| Autore | Bauer Heinz <1928-> |
| Edizione | [Reprint 2012] |
| Pubbl/distr/stampa | Berlin, [Germany] ; ; New York, [New York] : , : Walter de Gruyter, , 2003 |
| Descrizione fisica | 1 online resource (610 p.) |
| Disciplina | 515/.42 |
| Soggetto topico |
Integrals, Generalized
Measure theory Potential theory (Mathematics) Convex sets |
| Soggetto genere / forma | Electronic books. |
| ISBN | 3-11-089976-0 |
| Classificazione | SK 430 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- Preface -- Curriculum vitae -- Ph.D. students of Heinz Bauer -- Contents -- The work of Heinz Bauer in measure and integration / Chatterji, S. D. -- The work of Heinz Bauer in convexity theory / Edwards, D. A. -- The work of Heinz Bauer in potential theory / Netuka, Ivan -- Reguläre und singuläre Abbildungen eines distributiven Verbandes in einen vollständigen Vektorverband, welche der Funktionalgleichung f(x⋁y) + f(x⋀y) = f(x) + f(y) genügen [R3] -- Über die Beziehungen einer abstrakten Theorie des Riemann-Integrals zur Theorie Radonscher Maße [R9] -- Sur l'équivalence des théories de l'intégration selon N. Bourbaki et selon M. H. Stone [R10] -- Minimalstellen von Funktionen und Extremalpunkte [R13] -- Konservative Abbildungen lokal-kompakter Räume [R14] -- Minimalstellen von Funktionen und Extremalpunkte. II [R16] -- Šilovscher Rand und Dirichletsches Problem [R17] -- Axiomatische Behandlung des Dirichletschen Problems für elliptische und parabolische Differentialgleichungen [R19] -- Weiterführung einer axiomatischen Potentialtheorie ohne Kern (Existenz von Potentialen [R20] -- Kennzeichnung kompakter Simplexe mit abgeschlossener Extremalpunktmenge [R21] -- Propriétés fines des fonctions hyperharmoniques dans une théorie axiomatique du potentiel [R23] -- Zum Cauchyschen und Dirichletschen Problem bei elliptischen und parabolischen Differentialgleichungen [R24] -- Mesures avec une image donnée [R25] -- The part metric in convex sets [R26] -- An open mapping theorem for convex sets with only one part [R27] -- Theorems of Korovkin type for adapted spaces [R29] -- Convergence of monotone operators [R30] -- Korovkin approximation in C0(X) [R32] -- Approximation and abstract boundaries [S12] -- Halbgruppen und Resolventen in der Potentialtheorie [S15] -- Harmonic spaces - a survey [S21] -- Heat balls and Fulks measures [R34] -- Simplicial function spaces and simplexes [R35] -- Fine boundary limits of harmonic and caloric functions [R36] -- Simplices in potential theory [S24] -- Fine boundary limits and maximal sequences [R39] -- Behaviour of solutions of elliptic-parabolic differential equations at irregular boundary points [S26] -- Acknowledgements -- Bibliography |
| Record Nr. | UNINA-9910464143403321 |
|
Bauer Heinz <1928->
|
||
| Berlin, [Germany] ; ; New York, [New York] : , : Walter de Gruyter, , 2003 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Selecta / / Heinz Bauer ; edited by Herbert Heyer, Niels Jacob, Ivan Netuka
| Selecta / / Heinz Bauer ; edited by Herbert Heyer, Niels Jacob, Ivan Netuka |
| Autore | Bauer Heinz <1928-> |
| Edizione | [Reprint 2012] |
| Pubbl/distr/stampa | Berlin, [Germany] ; ; New York, [New York] : , : Walter de Gruyter, , 2003 |
| Descrizione fisica | 1 online resource (610 p.) |
| Disciplina | 515/.42 |
| Soggetto topico |
Integrals, Generalized
Measure theory Potential theory (Mathematics) Convex sets |
| ISBN | 3-11-089976-0 |
| Classificazione | SK 430 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- Preface -- Curriculum vitae -- Ph.D. students of Heinz Bauer -- Contents -- The work of Heinz Bauer in measure and integration / Chatterji, S. D. -- The work of Heinz Bauer in convexity theory / Edwards, D. A. -- The work of Heinz Bauer in potential theory / Netuka, Ivan -- Reguläre und singuläre Abbildungen eines distributiven Verbandes in einen vollständigen Vektorverband, welche der Funktionalgleichung f(x⋁y) + f(x⋀y) = f(x) + f(y) genügen [R3] -- Über die Beziehungen einer abstrakten Theorie des Riemann-Integrals zur Theorie Radonscher Maße [R9] -- Sur l'équivalence des théories de l'intégration selon N. Bourbaki et selon M. H. Stone [R10] -- Minimalstellen von Funktionen und Extremalpunkte [R13] -- Konservative Abbildungen lokal-kompakter Räume [R14] -- Minimalstellen von Funktionen und Extremalpunkte. II [R16] -- Šilovscher Rand und Dirichletsches Problem [R17] -- Axiomatische Behandlung des Dirichletschen Problems für elliptische und parabolische Differentialgleichungen [R19] -- Weiterführung einer axiomatischen Potentialtheorie ohne Kern (Existenz von Potentialen [R20] -- Kennzeichnung kompakter Simplexe mit abgeschlossener Extremalpunktmenge [R21] -- Propriétés fines des fonctions hyperharmoniques dans une théorie axiomatique du potentiel [R23] -- Zum Cauchyschen und Dirichletschen Problem bei elliptischen und parabolischen Differentialgleichungen [R24] -- Mesures avec une image donnée [R25] -- The part metric in convex sets [R26] -- An open mapping theorem for convex sets with only one part [R27] -- Theorems of Korovkin type for adapted spaces [R29] -- Convergence of monotone operators [R30] -- Korovkin approximation in C0(X) [R32] -- Approximation and abstract boundaries [S12] -- Halbgruppen und Resolventen in der Potentialtheorie [S15] -- Harmonic spaces - a survey [S21] -- Heat balls and Fulks measures [R34] -- Simplicial function spaces and simplexes [R35] -- Fine boundary limits of harmonic and caloric functions [R36] -- Simplices in potential theory [S24] -- Fine boundary limits and maximal sequences [R39] -- Behaviour of solutions of elliptic-parabolic differential equations at irregular boundary points [S26] -- Acknowledgements -- Bibliography |
| Record Nr. | UNINA-9910788709503321 |
|
Bauer Heinz <1928->
|
||
| Berlin, [Germany] ; ; New York, [New York] : , : Walter de Gruyter, , 2003 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Selecta / / Heinz Bauer ; edited by Herbert Heyer, Niels Jacob, Ivan Netuka
| Selecta / / Heinz Bauer ; edited by Herbert Heyer, Niels Jacob, Ivan Netuka |
| Autore | Bauer Heinz <1928-> |
| Edizione | [Reprint 2012] |
| Pubbl/distr/stampa | Berlin, [Germany] ; ; New York, [New York] : , : Walter de Gruyter, , 2003 |
| Descrizione fisica | 1 online resource (610 p.) |
| Disciplina | 515/.42 |
| Soggetto topico |
Integrals, Generalized
Measure theory Potential theory (Mathematics) Convex sets |
| ISBN | 3-11-089976-0 |
| Classificazione | SK 430 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- Preface -- Curriculum vitae -- Ph.D. students of Heinz Bauer -- Contents -- The work of Heinz Bauer in measure and integration / Chatterji, S. D. -- The work of Heinz Bauer in convexity theory / Edwards, D. A. -- The work of Heinz Bauer in potential theory / Netuka, Ivan -- Reguläre und singuläre Abbildungen eines distributiven Verbandes in einen vollständigen Vektorverband, welche der Funktionalgleichung f(x⋁y) + f(x⋀y) = f(x) + f(y) genügen [R3] -- Über die Beziehungen einer abstrakten Theorie des Riemann-Integrals zur Theorie Radonscher Maße [R9] -- Sur l'équivalence des théories de l'intégration selon N. Bourbaki et selon M. H. Stone [R10] -- Minimalstellen von Funktionen und Extremalpunkte [R13] -- Konservative Abbildungen lokal-kompakter Räume [R14] -- Minimalstellen von Funktionen und Extremalpunkte. II [R16] -- Šilovscher Rand und Dirichletsches Problem [R17] -- Axiomatische Behandlung des Dirichletschen Problems für elliptische und parabolische Differentialgleichungen [R19] -- Weiterführung einer axiomatischen Potentialtheorie ohne Kern (Existenz von Potentialen [R20] -- Kennzeichnung kompakter Simplexe mit abgeschlossener Extremalpunktmenge [R21] -- Propriétés fines des fonctions hyperharmoniques dans une théorie axiomatique du potentiel [R23] -- Zum Cauchyschen und Dirichletschen Problem bei elliptischen und parabolischen Differentialgleichungen [R24] -- Mesures avec une image donnée [R25] -- The part metric in convex sets [R26] -- An open mapping theorem for convex sets with only one part [R27] -- Theorems of Korovkin type for adapted spaces [R29] -- Convergence of monotone operators [R30] -- Korovkin approximation in C0(X) [R32] -- Approximation and abstract boundaries [S12] -- Halbgruppen und Resolventen in der Potentialtheorie [S15] -- Harmonic spaces - a survey [S21] -- Heat balls and Fulks measures [R34] -- Simplicial function spaces and simplexes [R35] -- Fine boundary limits of harmonic and caloric functions [R36] -- Simplices in potential theory [S24] -- Fine boundary limits and maximal sequences [R39] -- Behaviour of solutions of elliptic-parabolic differential equations at irregular boundary points [S26] -- Acknowledgements -- Bibliography |
| Record Nr. | UNINA-9910809891803321 |
|
Bauer Heinz <1928->
|
||
| Berlin, [Germany] ; ; New York, [New York] : , : Walter de Gruyter, , 2003 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Spaces of measures [[electronic resource] /] / Corneliu Constantinescu
| Spaces of measures [[electronic resource] /] / Corneliu Constantinescu |
| Autore | Constantinescu Corneliu |
| Edizione | [Reprint 2011] |
| Pubbl/distr/stampa | Berlin ; ; New York, : W. de Gruyter, 1984 |
| Descrizione fisica | 444 p |
| Disciplina | 515.42 |
| Collana | De Gruyter Studies in Mathematics |
| Soggetto topico |
Spaces of measures
Measure theory |
| ISBN | 3-11-085399-X |
| Classificazione | SK 430 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Introduction -- Logical connections between sections -- Notations and Terminology -- Chapter 1: Topological preliminaries -- Chapter 2: Spaces of functions -- Chapter 3: Spaces of supersummable families -- Chapter 4: Spaces of measures -- Chapter 5: Locally convex lattices -- References -- Index -- Notations -- Back matter |
| Record Nr. | UNINA-9910785843503321 |
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Constantinescu Corneliu
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| Berlin ; ; New York, : W. de Gruyter, 1984 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Young measures and compactness in measure spaces [[electronic resource] /] / Liviu C. Florescu, Christiane Godet-Thobie
| Young measures and compactness in measure spaces [[electronic resource] /] / Liviu C. Florescu, Christiane Godet-Thobie |
| Autore | Florescu Liviu C |
| Pubbl/distr/stampa | Berlin ; ; Boston, : De Gruyter, c2012 |
| Descrizione fisica | 1 online resource (352 p.) |
| Disciplina | 515/.42 |
| Altri autori (Persone) | Godet-ThobieChristiane |
| Soggetto topico |
Spaces of measures
Measure theory Mathematical optimization |
| Soggetto non controllato |
Bounded Measure
Functional Analysis Measure Space Topological Space Weak Compactness Young Measure |
| ISBN |
1-283-85791-X
3-11-028051-5 3-11-028052-3 |
| Classificazione | SK 430 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Preface -- Contents -- Chapter 1. Weak Compactness in Measure Spaces -- Chapter 2. Bounded Measures on Topological Spaces -- Chapter 3. Young Measures -- Bibliography -- Index -- About the Authors |
| Record Nr. | UNINA-9910790492103321 |
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Florescu Liviu C
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| Berlin ; ; Boston, : De Gruyter, c2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||