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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
Database:WorldCat
Summary:

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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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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