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Editorial Reviews
Review
"If I were asked to recommend texts to research students who need a grounding in integration theory this book would be on the list...The book is excellent" - C. Barnett, Imperial College of Science, Technology and Medicine, London
Product Description
This book is designed to be an introduction to analysis with the proper mix of abstract theories and concrete problems. It starts with general measure theory, treats Borel and Radon measures (with particular attention paid to Lebesgue measure) and introduces the reader to Fourier analysis in Euclidean spaces with a treatment of Sobolev spaces, distributions, and the Fourier analysis of such. It continues with a Hilbertian treatment of the basic laws of probability including Doob's martingale convergence theorem and finishes with Malliavin's "stochastic calculus of variations" developed in the context of Gaussian measure spaces. This invaluable contribution to the existing literature gives the reader a taste of the fact that analysis is not a collection of independent theories but can be treated as a whole.
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Inside This Book
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First Sentence:
Let X be an abstract set. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
exhaustion sequence, independent real random variables, narrow convergence, truncation operator, martingale relative, positive linear functional, convexity inequality, monotone class, negligible set, measurable mappings, finite additivity, locally compact space, probability space, measure space, unity subordinate Key Phrases - Capitalized Phrases (CAPs): (learn more)
Fatou-Beppo Levi, Laurent Schwartz, New York, General Topology New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Let X be an abstract set. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
exhaustion sequence, independent real random variables, narrow convergence, truncation operator, martingale relative, positive linear functional, convexity inequality, monotone class, negligible set, measurable mappings, finite additivity, locally compact space, probability space, measure space, unity subordinate Key Phrases - Capitalized Phrases (CAPs): (learn more)
Fatou-Beppo Levi, Laurent Schwartz, New York, General Topology New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 47
books:
See all 47 books this book cites
100
books
cite this book:
See all 100 books citing this book
- Real and Abstract Analysis (Graduate Texts in Mathematics) (v. 25) by Edwin Hewitt in Front Matter, and page 95
- Algebraic Topology: An Introduction (Graduate Texts in Mathematics) (v. 56) by William S. Massey in Front Matter
- Functions of One Complex Variable (Graduate Texts in Mathematics - Vol 11) (v. 1) by John B Conway in Front Matter
- Algebraic Geometry (Graduate Texts in Mathematics) by Robin Hartshorne in Front Matter
- Introduction to Operator Theory I. Elements of Functional Analysis by Arlen Brown in Front Matter
See all 47 books this book cites
- Measures, Integrals and Martingales by René L. Schilling in Back Matter (1), and Back Matter (2)
- Probability and Statistics by Example: Volume 1, Basic Probability and Statistics (v. 1) by Yuri Suhov in Back Matter
- 1,001 Low-Fat Vegetarian Recipes: Delicious, Easy-to-Make, Healthy Meals for Everyone by Sue Spitler on page 197
- Galois Theory (Graduate Texts in Mathematics) by Harold M. Edwards in Back Matter
- Optima and Equilibria: An Introduction to Nonlinear Analysis (Graduate Texts in Mathematics) by Jean-Pierre Aubin in Back Matter
See all 100 books citing this book
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