ABSTRACT

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 counterexample

chapter |38 pages

Introduction: basic concepts

chapter 1|24 pages

Cantor and Peano type functions

chapter 2|26 pages

Functions of first Baire class

chapter 4|18 pages

Singular monotone functions

chapter 9|24 pages

Hamel basis and Cauchy functional equation

chapter 11|14 pages

Absolutely nonmeasurable additive functions

chapter 12|18 pages

Egorov type theorems