Buch, Englisch, 584 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 934 g
Buch, Englisch, 584 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 934 g
Reihe: Studies in Advanced Mathematics
ISBN: 978-1-58488-073-8
Verlag: Chapman and Hall/CRC
Designed for use in a two-semester course on abstract analysis, REAL ANALYSIS: An Introduction to the Theory of Real Functions and Integration illuminates the principle topics that constitute real analysis. Self-contained, with coverage of topology, measure theory, and integration, it offers a thorough elaboration of major theorems, notions, and constructions needed not only by mathematics students but also by students of statistics and probability, operations research, physics, and engineering.Structured logically and flexibly through the author's many years of teaching experience, the material is presented in three main sections:Part 1, chapters 1through 3, covers the preliminaries of set theory and the fundamentals of metric spaces and topology. This section can also serves as a text for first courses in topology.Part II, chapter 4 through 7, details the basics of measure and integration and stands independently for use in a separate measure theory course.Part III addresses more advanced topics, including elaborated and abstract versions of measure and integration along with their applications to functional analysis, probability theory, and conventional analysis on the real line. Analysis lies at the core of all mathematical disciplines, and as such, students need and deserve a careful, rigorous presentation of the material. REAL ANALYSIS: An Introduction to the Theory of Real Functions and Integration offers the perfect vehicle for building the foundation students need for more advanced studies.
Zielgruppe
Mathematics, physics, statistics, and engineering students
Autoren/Hrsg.
Weitere Infos & Material
PART I. AN INTRODUCTION TO GENERAL TOPOLOGYSET-THEORETIC AND ALGEBRAIC PRELIMINARIESSets and Basic NotationFunctionsSet Operations under MapsRelations and Well-Ordering PrincipleCartesian ProductCardinalityBasic Algebraic StructuresANALYSIS OF METRIC SPACESDefinitions and NotationsThe Structure of Metric Spaces5Convergence in Metric SpacesContinuous Mappings in Metric SpacesComplete Metric SpacesCompactnessLinear and Normed Linear SpacesELEMENTS OF POINT SET TOPOLOGYTopological SpacesBases and Subbases for Topological SpacesConvergence of Sequences in Topological Spaces and CountabilityContinuity in Topological SpacesProduct TopologyNotes on Subspaces and CompactnesFunction Spaces and Ascoli's TheoremStone-Weierstrass Approximation TheoremFilter and Net ConvergenceSeparationFunctions on Locally Compact SpacesPART II. BASICS OF MEASURE AND INTEGRATIONMEASURABLE SPACES AND MEASURABLE FUNCTIONSSystems of SetsSystem's GeneratorsMeasurable FunctionsMEASURESSet FunctionsExtension of Set Functions to a MeasureLebesgue and Lebesgue-Stieltjes MeasuresImage MeasuresExtended Real-Valued Measurable FunctionsSimple FunctionsELEMENTS OF INTEGRATIONIntegration on C -1(W,S)Main Convergence TheoremsLebesgue and Riemann Integrals on RIntegration with Respect to Image MeasuresMeasures Generated by Integrals. Absolute Continuity.OrthogonalityProduct Measures of Finitely Many Measurable Spaces andFubini's TheoremApplications of Fubini's TheoremCALCULUS IN EUCLIDEAN SPACESDifferentiationChange of VariablesPART III. FURTHER TOPICS IN INTEGRATIONANALYSIS IN ABSTRACT SPACESSigned and Complex MeasuresAbsolute ContinuitySingularityLp SpacesModes of ConvergenceUniform IntegrabilityRadon Measures on Locally Compact Hausdorff SpacesMeasure DerivativesCALCULUS ON THE REAL LINEMonotone FunctionsFunctions of Bounded VariationAbsolute Continuous FunctionsSingular FunctionsBIBLIOGRAPHY
