โ Scribed by Alexander Kharazishvili
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Content: Machine generated contents note: ch. 0 Introduction: Basic concepts --
ch. 1 Cantor and Peano type functions --
ch. 2 Functions of first Baire class --
ch. 3 Semicontinuous functions that are not countably continuous --
ch. 4 Singular monotone functions --
ch. 5 A characterization of constant functions via Dini's derived numbers --
ch. 6 Everywhere differentiable nowhere monotone functions --
ch. 7 Continuous nowhere approximately differentiable functions --
ch. 8 Blumberg's theorem and Sierpinski-Zygmund functions --
ch. 9 The cardinality of first Baire class --
ch. 10 Lebesgue nonmeasurable functions and functions without the Baire property --
ch. 11 Hamel basis and Cauchy functional equation --
ch. 12 Summation methods and Lebesgue nonmeasurable functions --
ch. 13 Luzin sets, Sierpinski sets, and their applications --
ch. 14 Absolutely nonmeasurable additive functions --
ch. 15 Egorov type theorems --
ch. 16 A difference between the Riemann and Lebesgue iterated integrals --
ch. 17 Sierpinski's partition of the Euclidean plane --
ch. 18 Bad functions defined on second category sets --
ch. 19 Sup-measurable and weakly sup-measurable functions --
ch. 20 Generalized step-functions and superposition operators --
ch. 21 Ordinary differential equations with bad right-hand sides --
ch. 22 Nondifferentiable functions from the point of view of category and measure --
ch. 23 Absolute null subsets of the plane with bad orthogonal projections.
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Analyzes examples and constructions of strange functions. Explores the Axiom of Dependent Choice and demonstrates its sufficiency for most domains of classical mathematics. Highlights the general theory of stochastic processes. Contains more than 1400 equations.
<P><STRONG><EM>Strange Functions in Real Analysis, Third Edition</EM></STRONG> differs from the previous editions in that it includes five new chapters as well as two appendices. More importantly, the entire text has been revised and contains more detailed explanations of the presented material. In