Strange Functions in Real Analysis - Softcover

Kharazishvili, Alexander

Softcover

ISBN 10: 0367391465 ISBN 13: 9780367391461

Publisher: Chapman and Hall/CRC, 2019

Synopsis

Weierstrass and Blancmange nowhere differentiable functions, Lebesgue integrable functions with everywhere divergent Fourier series, and various nonintegrable Lebesgue measurable functions. While dubbed strange or "pathological," these functions are ubiquitous throughout mathematics and play an important role in analysis, not only as counterexamples of seemingly true and natural statements, but also to stimulate and inspire the further development of real analysis.

Strange Functions in Real Analysis explores a number of important examples and constructions of pathological functions. After introducing the basic concepts, the author begins with Cantor and Peano-type functions, then moves to functions whose constructions require essentially noneffective 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, he considers examples of functions whose existence cannot be established without the help of additional set-theoretical axioms and demonstrates that their existence follows from certain set-theoretical hypotheses, such as the Continuum Hypothesis.

About this title

About the Author

Kharazishvili, Alexander

Edition details

• Publisher: Chapman and Hall/CRC
• Publication date: 2019
• ISBN 10: 0367391465
• ISBN 13: 9780367391461
• Binding: Paperback
• Language: English
• Edition number: 2
• Number of pages: 432