Sulla misurabilita' delle funzioni di piu' variabili

LetE be a Lebesgue measurable set in IR ^p+q andY a metric space. Iff:E→Y is such thatf(.,x) isL-measurable for almost allx andf(t,.) is continuous in each of theq variables separately for almost allt, thenf must beL-measurable (Theorem 1). By this result we deduce that a functionf:E→Y is almost-continuous iff it is almost-separately continuous. Finally, we give another characterization of the measurability of a functionf:IRp+q ^p+q→Y by means of properties of its sections (Theorem 2).