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 ...
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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.
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Add this copy of Pure and Applied Mathematics: Strange Functions in Real to cart. $39.15, good condition, Sold by Anybook rated 4.0 out of 5 stars, ships from Lincoln, UNITED KINGDOM, published 2006 by Chapman & Hall.
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This is an ex-library book and may have the usual library/used-book markings inside. This book has hardback covers. In good all round condition. No dust jacket. Please note the Image in this listing is a stock photo and may not match the covers of the actual item, 900grams, ISBN: 9781584885825.
Add this copy of Strange Functions in Real Analysis (Pure & Applied to cart. $62.23, like new condition, Sold by Literary Cat Books rated 1.0 out of 5 stars, ships from Machynlleth, Powys, WALES, UNITED KINGDOM, published 2000 by Marcel Dekker.
Add this copy of Strange Functions in Real Analysis to cart. $79.04, new condition, Sold by Booksplease rated 4.0 out of 5 stars, ships from Southport, MERSEYSIDE, UNITED KINGDOM, published 2024 by CRC Press.
Add this copy of Strange Functions in Real Analysis. Second Edition to cart. $81.17, very good condition, Sold by Literary Cat Books rated 1.0 out of 5 stars, ships from Machynlleth, Powys, WALES, UNITED KINGDOM, published 2006 by Chapman and Hall/Crc.
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Add this copy of Strange Functions in Real Analysis, Second Edition to cart. $133.58, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Santa Clarita, CA, UNITED STATES, published 2005 by Chapman and Hall/CRC.
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