Counterexamples in Probability and Real Analysis

✍ Scribed by Gary L. Wise, Eric B. Hall

• Year: 1993
• Tongue: English
• Leaves: 224
• Category: Library

✦ Synopsis

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 in mathematical 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 argue convincingly 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 accessible for 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 want a copy of this book.

✦ Table of Contents

Contents......Page 10
Preface......Page 8
Notation......Page 12
I. The Counterexamples......Page 16
II. The Counterexamples with Proofs......Page 18
1. The Real Line......Page 46
2. Real–Valued Functions......Page 66
3. Differentiation......Page 84
4. Measures......Page 94
5. Integration......Page 116
6. Product Spaces......Page 134
7. Basic Probability......Page 150
8. Conditioning......Page 172
9. Convergence in Probability Theory......Page 184
10. Applications of Probability......Page 196
E......Page 222
O......Page 223
Z......Page 224

✦ Subjects

Математика;Теория вероятностей и математическая статистика;Теория вероятностей;