04978nam 22014895 450 991015474320332120190708092533.01-4008-8232-X10.1515/9781400882328(CKB)3710000000631387(MiAaPQ)EBC4738703(DE-B1597)468033(OCoLC)979970577(DE-B1597)9781400882328(EXLCZ)99371000000063138720190708d2016 fg engurcnu||||||||rdacontentrdamediardacarrierSurface Area. (AM-35), Volume 35 /Lamberto CesariPrinceton, NJ : Princeton University Press, [2016]©19571 online resource (612 pages) illustrationsAnnals of Mathematics Studies ;3430-691-09585-X Includes bibliography.Frontmatter -- PREFACE -- CONTENTS -- CHAPTER I. INTRODUCTORY- CONSIDERATIONS -- CHAPTER II. LEBESGUE AREA -- CHAPTER III. THE GEÖCZE AREAS V AND U AND THE PEANO AREA P -- CHAPTER IV. BV AND AC PLANE MAPPINGS -- CHAPTER V. THE FIRST THEOREM -- CHAPTER VI. THE CAVALIERI INEQUALITY -- CHAPTER VII. IDENTIFICATION OF LEBESGUE, GEÖCZE, PEANO AREAS -- CHAPTER VIII. GEOMETRICAL PROPERTIES AND THE SECOND THEOREM -- CHAPTER IX. THE REPRESENTATION PROBLEM -- CHAPTER X. THE REPRESENTATION OF GENERAL SURFACES AND THE THIRD THEOREM -- APPENDIX A. A DIRECT PROOF OF A PROPERTY OF CONTINUOUS SURFACES -- APPENDIX B. WEIERSTRASS INTEGRAL OVER A SURFACE -- BIBLIOGRAPHY -- SPECIAL SIGNS AND ABBREVIATIONS -- BackmatterThe description for this book, Surface Area. (AM-35), Volume 35, will be forthcoming.Annals of mathematics studies ;no. 35.SurfacesAbsolute continuity.Addition.Admissible set.Arc length.Axiom.Axiomatic system.Bearing (navigation).Bounded variation.Calculus of variations.Circumference.Compact space.Complex analysis.Concentric.Connected space.Continuous function (set theory).Continuous function.Corollary.Countable set.Covering set.Curve.Derivative.Diameter.Differentiable function.Differential geometry.Direct proof.Dirichlet integral.Disjoint sets.Empty set.Equation.Equicontinuity.Existence theorem.Existential quantification.Function (mathematics).Functional analysis.Geometry.Hausdorff measure.Homeomorphism.Homotopy.Infimum and supremum.Integral geometry.Intersection number (graph theory).Interval (mathematics).Iterative method.Jacobian.Lebesgue integration.Lebesgue measure.Limit (mathematics).Limit point.Limit superior and limit inferior.Linearity.Line–line intersection.Locally compact space.Mathematician.Mathematics.Measure (mathematics).Metric space.Morphism.Natural number.Nonparametric statistics.Orientability.Parameter.Parametric equation.Parametric surface.Partial derivative.Potential theory.Radon–Nikodym theorem.Representation theorem.Representation theory.Right angle.Semi-continuity.Set function.Set theory.Sign (mathematics).Smoothness.Space-filling curve.Subset.Summation.Surface area.Tangent space.Theorem.Topological space.Topology.Total order.Total variation.Uniform convergence.Unit square.Surfaces.516.36Cesari Lamberto, 40585DE-B1597DE-B1597BOOK9910154743203321Surface Area. (AM-35), Volume 352786533UNINA