Strange Functions in Real Analysis, Third Edition differs from the previous editions in that it includes five new chapters as well as two appendices. More importantly, the entire text has been revised and contains more detailed explanations of the presented material. In doing so, the book explores a number of important examples and constructions of pathological functions.

After introducing basic concepts, the author begins with Cantor and Peano-type functions, then moves effortlessly to functions whose constructions require what is essentially non-effective methods. These include functions without the Baire property, functions associated with a Hamel basis of the real line and Sierpinski-Zygmund functions that are discontinuous on each subset of the real line having the cardinality continuum.

Finally, the author considers examples of functions whose existence cannot be established without the help of additional set-theoretical axioms. On the whole, the book is devoted to strange functions (and point sets) in real analysis and their applications.

Reviews

This is the third edition of a text based on the author's lectures at Tiblisi University, Georgia. While of interest in themselves, the "strange functions" alluded to in the title can serve as counterexamples to hypotheses that on first consideration appear reasonable. Thus, they inform mathematical thinking in the field. The text also provides the mathematical framework used to develop and validate these strange functions. Other reviewers of past editions of this book have observed that it is similar in concept to J. C. Oxtoby's Measure and Category (1971). This edition contains more examples and is substantially longer than Oxtoby's. Kharazishvili has added five chapters and two appendixes to the second edition (2005) and presents a fairly complete revision of that edition. While this work is as much a reference as it is a textbook, it contains a number of exercises as well as an extensive bibliography. This text is recommended for advanced mathematics collections, though there may not be sufficient new material to justify replacing the previous edition.

--D. Z. Spicer, University System of Maryland, Choice Connect

Book Information
ISBN 9781032919881
Author Alexander Kharazishvili
Format Paperback
Page Count 440
Imprint Chapman & Hall/CRC
Publisher Taylor & Francis Ltd
Weight(grams) 810g