A. GAVRILUŢ, A. CROITORU Faculty of Mathematics, "Al.I. Cuza" University, Carol I Bd. 11, IaĹi, 700506, România, email: gavrilut@uaic.ro, croitoru@uaic.ro
In this paper, we study different basic problems concerning real valued functions which are totally-measurable with respect to the variation of a (multi)submeasure. As applications, special considerations on their relation with Gould type integrability and additional problems are given (e.g., a Fatou lemma type, the Banach structure of a Lp space).