Counterexamples In Measure And Integration
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Counterexamples in Measure and Integration
Author: René L. Schilling
language: en
Publisher: Cambridge University Press
Release Date: 2021-06-17
Explore measure and integration theory by asking 'What can go wrong if...' with this selection of over 300 counterexamples.
Counterexamples in Measure and Integration
Author: René L. Schilling
language: en
Publisher: Cambridge University Press
Release Date: 2021-06-17
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 René Schilling's other book Measures, Integrals and Martingales (www.cambridge.org/9781316620243).
Counterexamples in Analysis
Author: Bernard R. Gelbaum
language: en
Publisher: Courier Corporation
Release Date: 2003-06-04
These counterexamples deal mostly with the part of analysis known as "real variables." The 1st half of the book discusses the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, more. The 2nd half examines functions of 2 variables, plane sets, area, metric and topological spaces, and function spaces. 1962 edition. Includes 12 figures.