Counterexamples in Probability and Real Analysis

Hardcover | October 1, 1994

byGary L. Wise, Eric B. Hall

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A counterexample is any example or result that is the opposite of one's intuition or to commonly held beliefs. Counterexamples can have great educational value in illuminating complex topics that are difficult to explain in a rigidly logical, written presentation. For example, ideas inmathematical sciences that might seem intuitively obvious may be proved incorrect with the use of a counterexample. This monograph concentrates on counterexamples for use at the intersection of probability and real analysis, which makes it unique among such treatments. The authors argueconvincingly that probability theory cannot be separated from real analysis, and this book contains over 300 examples related to both the theory and application of mathematics. Many of the examples in this collection are new, and many old ones, previously buried in the literature, are now accessiblefor the first time. In contrast to several other collections, all of the examples in this book are completely self-contained--no details are passed off to obscure outside references. Students and theorists across fields as diverse as real analysis, probability, statistics, and engineering will wanta copy of this book.

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From the Publisher

A counterexample is any example or result that is the opposite of one's intuition or to commonly held beliefs. Counterexamples can have great educational value in illuminating complex topics that are difficult to explain in a rigidly logical, written presentation. For example, ideas inmathematical sciences that might seem intuitively...

Gary L. Wise is at University of Texas, Austin. Eric B. Hall is at Southern Methodist University.

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Format:HardcoverDimensions:224 pages, 9.49 × 6.3 × 0.91 inPublished:October 1, 1994Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0195070682

ISBN - 13:9780195070682

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Table of Contents

1. The Real Line2. Real Valued Functions3. Differentiation4. Measures5. Integration6. Product Spaces7. Basic Probability8. Conditioning9. Convergence in Probability10. Applications of Probability

Editorial Reviews

"Will be of a great deal of interest to analysts and some probabilists." --Mathematical Reviews