584 Pages
by
CRC Press
584 Pages
by
CRC Press
584 Pages
by
CRC Press
Also available as eBook on:
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: Providing a fundamental, modern approach to measure theory... Read more
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
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
Biography
Kenneth Kuttler
"A lucid and effective presentation of...sophisticated material"
- Joseph A. Cima, Department of Mathematics, University of North Carolina, Chapel Hill
"Ambitious...Conversant...Great"
Steven G. Krantz, Department of Math, Washington University, St. Louis, Missouri
"The author has chosen his topics well to demonstrate how even the oldest subjects can have a "modern" approach that improves on the original. The text is all business and very readable, especially for the mathematically prepared reader. There is a lot to recommend from the use of this book, not the least of which is the fact that the reader participates in the continuing documentation of "modern" mathematical analysis."
-Timothy Hall, PQI Consulting
