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Counterexamples in Measure and Integration (Hardcover)
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Counterexamples in Measure and Integration (Hardcover)
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Often it is more instructive to know 'what can go wrong' and to
understand 'why a result fails' than to plod through yet another
piece of theory. In this text, the authors gather more than 300
counterexamples - some of them both surprising and amusing -
showing the limitations, hidden traps and pitfalls of measure and
integration. Many examples are put into context, explaining
relevant parts of the theory, and pointing out further reading. The
text starts with a self-contained, non-technical overview on the
fundamentals of measure and integration. A companion to the
successful undergraduate textbook Measures, Integrals and
Martingales, it is accessible to advanced undergraduate students,
requiring only modest prerequisites. More specialized concepts are
summarized at the beginning of each chapter, allowing for
self-study as well as supplementary reading for any course covering
measures and integrals. For researchers, it provides ample examples
and warnings as to the limitations of general measure theory. This
book forms a sister volume to Rene Schilling's other book Measures,
Integrals and Martingales (www.cambridge.org/9781316620243).
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