Skip to content

Online ordering will be unavailable on Saturday 10 December 2022, 0800-1800 GMT.

To place an order, please contact Customer Services.

UK/ROW +44 (0) 1223 326050 | US 1 800 872 7423 or 1 212 337 5000 | Australia/New Zealand 61 3 86711400 or 1800 005 210, New Zealand 0800 023 520

Register Sign in Wishlist
Real Analysis and Probability

Real Analysis and Probability

2nd Edition


Part of Cambridge Studies in Advanced Mathematics

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


Add to wishlist

Other available formats:
Hardback, eBook

Looking for an inspection copy?

This title is not currently available on inspection

Product filter button
About the Authors
  • 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
    Read more

    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

    See more reviews

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity


    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?


    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

  • Author

    R. M. Dudley, Massachusetts Institute of Technology

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner Please see the permission section of the catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×
warning icon

Turn stock notifications on?

You must be signed in to your Cambridge account to turn product stock notifications on or off.

Sign in Create a Cambridge account arrow icon

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.


Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

Please fill in the required fields in your feedback submission.