Revival: Modern Analysis (1997) CRC Press Revivals Series
Auteur : Kuttler Kenneth
Modern Analysis provides coverage of real and abstract analysis, offering a sensible introduction to functional analysis as well as a thorough discussion of measure theory, Lebesgue integration, and related topics. This significant study clearly and distinctively presents the teaching and research literature of graduate analysis:
With an ambitious scope, this resource unifies various topics into one volume succinctly and completely. The contents span basic measure theory in an abstract and concrete form, material on classic linear functional analysis, probability, and some major results used in the theory of partial differential equations. Two different proofs of the central limit theorem are examined as well as a straightforward approach to conditional probability and expectation.
Modern Analysis provides ample and well-constructed exercises and examples. Introductory topology is included to help the reader understand such items as the Riesz theorem, detailing its proofs and statements. This work will help readers apply measure theory to probability theory, guiding them to understand the theorems rather than merely follow directions.
Preface
Set Theory and General Topology
Compactness and Continuous Functions
Banach Spaces
Hilbert Spaces
Calculus in Banach Space
Locally Convex Topological Vector Spaces
Measures and Measurable Functions
The Abstract Lebesgue Integral
The Construction of Measures
Lebesgue Measure
Product Measure
The Lp Spaces
Representation Theorems
Fundamental Theorem of Calculus
General Radon Measures
Fourier Transforms
Probability
Weak Derivatives
Hausdorff Measures
The Area Formula
The Coarea Formula
Fourier Analysis in Rn
Integration for Vector Valued Functions
Convex Functions
Appendix 1: The Hausdorff Maximal Theorem
Appendix 2: Stone's Theorem and Partitions of Unity
Appendix 3: Taylor Series and Analytic Functions
Appendix 4: The Brouwer Fixed Point Theorem
References
Index
Date de parution : 09-2017
15.6x23.4 cm
Date de parution : 01-2019
15.6x23.4 cm
Thème de Revival: Modern Analysis (1997) :
Mots-clés :
Banach Space; Borel Set; Bochner; Normed Linear Space; Milhin; Riesz Representation Theorem; Riesz; Lebesgue Measurable; Lebesgue; Dominated Convergence Theorem; Statistics; Monotone Class; Steven G; Krantz; Cauchy Sequence; Lebesgue Measurable Set; Topological Vector Space; Open Set; Measure Space; Metric Space; Finite Measure Spaces; Locally Convex Topological Vector Space; Uniform Convexity; Nonnegative Simple Function; Outer Measure; Radon Measure; Topological Space; Ascoli Arzela Theorem; Reflexive Banach Space; Radon Nikodym Theorem; Disjoint Balls; Borel Measurable Function