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Real Analysis and Probability : Cambridge Studies in Advanced Mathematics - R. M. Dudley

Real Analysis and Probability

Cambridge Studies in Advanced Mathematics

Hardcover

Published: 22nd December 2003
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This classic textbook, now reissued, offers a clear exposition of modern probability theory and of the interplay between the properties of metric spaces and probability measures. The new edition has been made even more self-contained than before; it now includes a foundation of the real number system and the Stone-Weierstrass theorem on uniform approximation in algebras of functions. Several other sections have been revised and improved, and the comprehensive historical notes have been further amplified. A number of new exercises have been added, together with hints for solution.

'A marvellous work which will soon become a standard text in the field for both teaching and reference ... a complete and pedagogically perfect presentation of both the necessary preparatory material of real analysis and the proofs throughout the text. Some of the topics and proofs are rarely found in other textbooks.' Proceedings of the Edinburgh Mathematical Society 'Careful, scholarly, and stimulating. It would be a pleasure to teach a mathematically-oriented graduate-level course from this text.' Short Book Reviews of the ISI '[It] will serve for a long time as a standard reference.' Zentralblatt fur und ihre Grenzgebiete 'What makes the book special ... is the care and scholarship with which the material is treated, and the choice of additional topics ... not usually covered in first year graduate courses.' Mathematical Reviews 'The book serves as a clear, rigorous, and complete introduction to modern probability theory using methods of mathematical analysis, and a description of relations between the two fields ... it could be very useful for students interested in learning both topics, it can also serve as complementary reading to standard lectures. Teachers preparing their graduate level courses can use the book as an excellent, rigorously written and complete source.' EMS Newsletter

Foundations: set theory
General topology
Measures
Integration
Lp spaces: introduction to functional analysis
Convex sets and duality of normed spaces
Measure, topology, and differentiation
Introduction to probability theory
Convergence of laws and central limit theorems
Conditional expectations and martingales
Convergence of laws on separable metric spaces
Stochastic processes
Measurability: Borel isomorphism and analytic sets
Appendixes
Axiomatic set theory
B
C
D
E
Indices
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521809726
ISBN-10: 052180972X
Series: Cambridge Studies in Advanced Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 568
Published: 22nd December 2003
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 22.8 x 15.2  x 4.0
Weight (kg): 1.03
Edition Number: 2
Edition Type: Revised