Description
Strange Functions in Real Analysis (2nd Ed.)
Author: Kharazishvili Alexander
Language: EnglishSubjects for Strange Functions in Real Analysis:
Keywords
Baire Property; Topological Space; Lebesgue Measure; Martin’s Axiom; Lebesgue Sense; Lebesgue Measurable Functions; Borel Subset; Nonempty Perfect Set; Nonempty Perfect Subset; Transfinite Recursion; Lebesgue Nonmeasurable Subset; Banach Space; Diffused Borel Measure; Cauchy Functional Equation; Ordinary Differential Equations; Generalized Luzin Set; Ordinal Number; Luzin Set; Uncountable Polish Space; Category Subset; Closed Subset; Borel Mapping; Cantor Discontinuum; Lebesgue Measurable Sets; Metric Space
Publication date: 09-2019
· 15.2x22.9 cm · Paperback
Approximative price 148.72 €
Subject to availability at the publisher.
Add to cart the book of Kharazishvili AlexanderPublication date: 01-2006
400 p. · 15x23 cm · Hardback
Description
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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.