On some analogies between measure and category and their applications in the theory of additive functions

Abstract

The firs t p a r t of the pape r is devoted to topological analogies of some theorems from re a l analysis (Vitali’s covering theorem, Lebesgue theorem o n oute r density, Smital’s lemma). Then we give a topological analogue of a theorem of Ostrowski connected with additive functions. In the la st p a r t we deal w ith Hamel bases, specially w ith Burstin bases. We prove th e ir existence and study topological and measure properties.