Abstract. The notion of a generalized sequence of Colombeau's generalized functions is introduced and studied. A weakly convergent sequence of Schwartz's distributions which is not an almost constant one does not determine a convergent sequence of Colombeau's generalized functions but it determines a weakly or h-weakly convergent generalized sequence of Colombeau's generalized functions.

AMS Subject Classification (1991): 46F05, 03H05

Keyword(s): Generalized functions, convergence, non-standard analysis

Received May 5, 1995 and in revised form October 11, 1995. (Registered under 5721/2009.)