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.
Lebesgue measure, additive function, extension of measure, absolutely nonmeasurable function.
MSC 2000: 28A05, 28D05.