On some analogies between measure and category and their applications in the theory of additive functions - Kuczma, Marek (Annales Mathematicae Silesianae, 1985)
The first part of the paper is devoted to topological analogies of some theorems from real analysis (Vitali’s covering theorem, Lebesgue theorem on outer density, Smital’s lemma). Then we give a topological analogue of a theorem of Ostrowski connected with additive functions. In the last part we deal with Hamel bases, specially with Burstin bases. We prove their existence and study topological and measure properties.