Absolutely nonmeasurable additive Sierpiński-Zygmund functions

Abstract

Here we will focus our consideration on functions acting from R into R and having bad structural properties (cf. Chapters 1 and 5). First of all, we mean those properties of functions which are bad from the measure-theoretical point of view. Notice that from the stand-point of general topology, bad functions are those which do not possess the Baire property. Notice also that, in many respects, the Baire property can be treated as a natural topological analogue of measurability (see, for instance, [40], [143], [148], [176], and [192]).