In the late 19th century, Karl Weierstrass invented a fractal-like function that was decried as nothing less than a “deplorable evil.” In time, it would transform the foundations of mathematics.

Various classes of analytic, quasi-analytic and other infinitely differentiable functions of a real variable are studied. The paper gives a self-contained treatment by means of an elementary real ...

We develop a partitioning lemma (see Lemma 5) for superadditive set functions satisfying certain continuity conditions. This leads to a relatively simple proof of two theorems of A. S. Besicovitch on ...