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Real Analysis and Probability

Real Analysis and Probability

2nd Edition

$69.99

Part of Cambridge Studies in Advanced Mathematics

  • Date Published: October 2002
  • availability: Available
  • format: Paperback
  • isbn: 9780521007542

$ 69.99
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  • This classic textbook offers a clear exposition of modern probability theory and of the interplay between the properties of metric spaces and probability measures. The first half of the book gives an exposition of real analysis: basic set theory, general topology, measure theory, integration, an introduction to functional analysis in Banach and Hilbert spaces, convex sets and functions and measure on topological spaces. The second half introduces probability based on measure theory, including laws of large numbers, ergodic theorems, the central limit theorem, conditional expectations and martingale's convergence. A chapter on stochastic processes introduces Brownian motion and the Brownian bridge. The 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.

    • Classic text by top-name author
    • Comprehensive treatment makes it also a useful reference
    • Over 400 exercises, many with hints for solutions
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    Reviews & endorsements

    '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

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    Product details

    • Edition: 2nd Edition
    • Date Published: October 2002
    • format: Paperback
    • isbn: 9780521007542
    • length: 566 pages
    • dimensions: 246 x 156 x 28 mm
    • weight: 0.77kg
    • contains: 400 exercises
    • availability: Available
  • Table of Contents

    1. Foundations: set theory
    2. General topology
    3. Measures
    4. Integration
    5. Lp spaces: introduction to functional analysis
    6. Convex sets and duality of normed spaces
    7. Measure, topology, and differentiation
    8. Introduction to probability theory
    9. Convergence of laws and central limit theorems
    10. Conditional expectations and martingales
    11. Convergence of laws on separable metric spaces
    12. Stochastic processes
    13. Measurability: Borel isomorphism and analytic sets
    Appendixes: A. Axiomatic set theory
    B. Complex numbers, vector spaces, and Taylor's theorem with remainder
    C. The problem of measure
    D. Rearranging sums of nonnegative terms
    E. Pathologies of compact nonmetric spaces
    Indices.

  • Author

    R. M. Dudley, Massachusetts Institute of Technology

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