Strange Functions in Real Analysis

Description

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.