A. Kharazishvili

On Absolutely Nonmeasurable Additive Functions

Abstract:
It is shown, under Martin's Axiom, that there exist absolutely nonmeasurable additive functions. Starting with this fact, a generalization of the well-known result of Pelc and Prikry (1983) is obtained. Some related questions concerning the measurability of additive functions are also discussed.

Keywords:
Lebesgue measure, additive function, extension of measure, absolutely nonmeasurable function.

MSC 2000: 28A05, 28D05.