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Strange functions in real analysis

Author: A B Kharazishvili
Publisher: Boca Raton, FL : Chapman & Hall/CRC, 2006.
Series: Monographs and textbooks in pure and applied mathematics, 272.
Edition/Format:   Print book : English : 2nd edView all editions and formats
Summary:
"This book explores strange functions in real analysis and their applications. This book presents basic set-theoretical concepts such as binary relations of special type and the Generalized Continuum Hypothesis. It examines various functions whose constructions need essentially noneffective methods and those whose existence arises from known hypotheses. It also discusses basic concepts of general topology and  Read more...
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: A B Kharazishvili
ISBN: 1584885823 9781584885825
OCLC Number: 61500096
Description: xii, 415 pages ; 24 cm.
Contents: Cantor and Peano type functions --
Functions of first Baire class --
Semicontinuous functions that are not countably continuous --
Singular monotone functions --
Everywhere differentiable nowhere monotone functions --
Nowhere approximately differentiable functions --
Blumberg's theorum and Sierpiński-Zygmund functions --
Lebesgue nonmeasurable functions and functions without the Baire property --
Hamel basis and Cauchy functional equation --
Luzin sets, Sierpiński sets, and their applications --
Absolutely nonmeasurable additive functions --
Egorov type theorems --
Sierpiński's partition of the Euclidean plane --
Bad functions defined on second category sets --
Sup-measurable and weakly sup-measurable functions --
Generalized step-functions and superposition operators --
Ordinary differential equations with bad right-hand sides --
Nondifferentiable functions from the point of view of category and measure.
Series Title: Monographs and textbooks in pure and applied mathematics, 272.
Responsibility: A.B. Kharazishvili.
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Abstract:

Explores a number of important examples and constructions of pathological functions. This work begins with Cantor and Peano-type functions and moves to functions whose constructions require  Read more...

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