Ideas in mathematical science that might seem intuitively obvious may be proved incorrect with the use of their counterexamples. This monograph concentrates on counterexamples utilized at the intersection of probability and real analysis.
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.
an interesting and informative book ... The book is self-contained and the material is presented with great clarity. The reader will find that it is stimulating and thought provoking ... Highly recommended for college and university libraries with graduate programs in mathematical sciences.
