Most mathematical examples illustrate the truth of a statement; counterexamples demonstrate a statement's falsity. This third edition features the author's revisions and corrections plus a substantial new appendix. 2012 edition.

This volume contains six early mathematical works, four papers on fiducial inference, five on transformations, and twenty-seven on a miscellany of topics in mathematical statistics. Several previously unpublished works are included.

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.

Counterexamples (in the mathematical sense) are powerful tools of mathematical theory. This book covers counterexamples from probability theory and stochastic processes. This new expanded edition includes many examples and the latest research results. The author is regarded as one of the foremost experts in the field. Contains numbers examples.

Over 140 examples, preceded by a succinct exposition of general topology and basic terminology. Each example treated as a whole. Numerous problems and exercises correlated with examples. 1978 edition. Bibliography.

These counterexamples deal mostly with the part of analysis known as "real variables." Covers the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, functions of 2 variables, plane sets, more. 1962 edition.

Approximately 1,000 problems — with answers and solutions included at the back of the book — illustrate such topics as random events, random variables, limit theorems, Markov processes, and much more.