INTEGRAL AND FUNCTIONAL ANALYSIS (UPDATED EDITION)
XIAO, JIE.
INTEGRAL AND FUNCTIONAL ANALYSIS (UPDATED EDITION) - 1 online resource - Mathematics Research Developments Ser. .
Includes bibliographies and index.
Intro -- INTEGRAL AND FUNCTIONALANALYSIS(UPDATED EDITION) -- INTEGRAL AND FUNCTIONALANALYSIS(UPDATED EDITION) -- Contents -- Preface -- Acknowledgments -- Chapter 1Preliminaries -- 1.1 Sets, Relations, Functions, Cardinals and Ordinals -- 1.2 Reals, Some Basic Theorems and Sequence Limits -- Problems -- Chapter 2Riemann Integrals -- 2.1 Definitions, Examples and Basic Properties -- 2.2 Algebraic Operations and the Darboux Criterion -- 2.3 Fundamental Theorem of Calculus -- 2.4 Improper Integrals -- Problems -- Chapter 3Riemann-Stieltjes Integrals -- 3.1 Functions of Bounded Variation 3.2 Definition and Basic Properties -- 3.3 Nonexistence and Existence for Integrals -- 3.4 Evaluations of Integrals -- 3.5 Improper Situations -- Problems -- Chapter 4Lebesgue-Radon-StieltjesIntegrals -- 4.1 Foundational Material -- 4.2 Essential Properties -- 4.3 Convergence Theorems -- 4.4 Extension via Measurability -- 4.5 Double, Iterated and Generic Integrals -- Problems -- Chapter 5Absolute Continuitiesin Lebesgue Integrals -- 5.1 Lebesgue's Outer Measure and Vitali's Covering -- 5.2 Derivatives of Increasing Functions -- 5.3 Absolutely Continuous Functions 5.4 Cantor's Ternary Set and Singular Function -- 5.5 Lebesgue's Points -- Problems -- Chapter 6Metric Spaces -- 6.1 Metrizable Topology and Connectedness -- 6.2 Completeness -- 6.3 Compactness, Density and Separability -- Problems -- Chapter 7Continuous Mappings -- 7.1 Criteria for Continuity -- 7.2 Continuous Mappings over Compactor ConnectedMetric Spaces -- 7.3 Sequences of Mappings -- 7.4 Contractions -- 7.5 Structures of Metric Spaces -- Problems -- Chapter 8Normed Linear Spaces -- 8.1 Linear Spaces, Norms and Quotient Spaces -- 8.2 Finite Dimensional Spaces -- 8.3 Bounded Linear Operators 8.4 Linear Functionals via Hahn-Banach Extension -- Problems -- Chapter 9Banach Spaces via Operatorsand Functionals -- 9.1 Definition and Beginning Examples -- 9.2 Uniform Boundedness -- Open Map -- Closed Graph -- 9.3 Dual Banach Spaces by Examples -- 9.4 Weak and Weak* Topologies -- 9.5 Compact and Dual Operators -- Problems -- Chapter 10Hilbert Spaces and TheirOperators -- 10.1 Definition, Examples and Basic Properties -- 10.2 Orthogonality, Orthogonal Complementand Duality -- 10.3 Orthonormal Sets and Bases -- 10.4 Five Special Bounded Operators -- 10.5 Compact Operators via Spectrum -- Problems Hints or Solutions -- 1 Preliminaries -- 3 Riemann-Stieltjes Integrals -- 4 Lebesgue-Radon-Stieltjes Integrals -- 5 Absolute Continuities in Lebesgue Integrals -- 6 Metric Spaces -- 7 Continuous Mappings -- 8 Normed Linear Spaces -- 9 Banach Spaces via Operators and Functionals -- 10 Hilbert Spaces and Their Operators -- 2 Riemann Integrals -- References -- About the Author -- Index -- Blank Page -- Blank Page
9781536196177
Integral equations.
Metric spaces.
Functional analysis.
Electronic Books.
QA431 / .I584 2021
INTEGRAL AND FUNCTIONAL ANALYSIS (UPDATED EDITION) - 1 online resource - Mathematics Research Developments Ser. .
Includes bibliographies and index.
Intro -- INTEGRAL AND FUNCTIONALANALYSIS(UPDATED EDITION) -- INTEGRAL AND FUNCTIONALANALYSIS(UPDATED EDITION) -- Contents -- Preface -- Acknowledgments -- Chapter 1Preliminaries -- 1.1 Sets, Relations, Functions, Cardinals and Ordinals -- 1.2 Reals, Some Basic Theorems and Sequence Limits -- Problems -- Chapter 2Riemann Integrals -- 2.1 Definitions, Examples and Basic Properties -- 2.2 Algebraic Operations and the Darboux Criterion -- 2.3 Fundamental Theorem of Calculus -- 2.4 Improper Integrals -- Problems -- Chapter 3Riemann-Stieltjes Integrals -- 3.1 Functions of Bounded Variation 3.2 Definition and Basic Properties -- 3.3 Nonexistence and Existence for Integrals -- 3.4 Evaluations of Integrals -- 3.5 Improper Situations -- Problems -- Chapter 4Lebesgue-Radon-StieltjesIntegrals -- 4.1 Foundational Material -- 4.2 Essential Properties -- 4.3 Convergence Theorems -- 4.4 Extension via Measurability -- 4.5 Double, Iterated and Generic Integrals -- Problems -- Chapter 5Absolute Continuitiesin Lebesgue Integrals -- 5.1 Lebesgue's Outer Measure and Vitali's Covering -- 5.2 Derivatives of Increasing Functions -- 5.3 Absolutely Continuous Functions 5.4 Cantor's Ternary Set and Singular Function -- 5.5 Lebesgue's Points -- Problems -- Chapter 6Metric Spaces -- 6.1 Metrizable Topology and Connectedness -- 6.2 Completeness -- 6.3 Compactness, Density and Separability -- Problems -- Chapter 7Continuous Mappings -- 7.1 Criteria for Continuity -- 7.2 Continuous Mappings over Compactor ConnectedMetric Spaces -- 7.3 Sequences of Mappings -- 7.4 Contractions -- 7.5 Structures of Metric Spaces -- Problems -- Chapter 8Normed Linear Spaces -- 8.1 Linear Spaces, Norms and Quotient Spaces -- 8.2 Finite Dimensional Spaces -- 8.3 Bounded Linear Operators 8.4 Linear Functionals via Hahn-Banach Extension -- Problems -- Chapter 9Banach Spaces via Operatorsand Functionals -- 9.1 Definition and Beginning Examples -- 9.2 Uniform Boundedness -- Open Map -- Closed Graph -- 9.3 Dual Banach Spaces by Examples -- 9.4 Weak and Weak* Topologies -- 9.5 Compact and Dual Operators -- Problems -- Chapter 10Hilbert Spaces and TheirOperators -- 10.1 Definition, Examples and Basic Properties -- 10.2 Orthogonality, Orthogonal Complementand Duality -- 10.3 Orthonormal Sets and Bases -- 10.4 Five Special Bounded Operators -- 10.5 Compact Operators via Spectrum -- Problems Hints or Solutions -- 1 Preliminaries -- 3 Riemann-Stieltjes Integrals -- 4 Lebesgue-Radon-Stieltjes Integrals -- 5 Absolute Continuities in Lebesgue Integrals -- 6 Metric Spaces -- 7 Continuous Mappings -- 8 Normed Linear Spaces -- 9 Banach Spaces via Operators and Functionals -- 10 Hilbert Spaces and Their Operators -- 2 Riemann Integrals -- References -- About the Author -- Index -- Blank Page -- Blank Page
9781536196177
Integral equations.
Metric spaces.
Functional analysis.
Electronic Books.
QA431 / .I584 2021