Abstract. We show the existence of sequences of rest bounded variation which cannot be decomposed into a monotonic sequence and a sequence having terms whose sum is absolute convergent. Furthermore we give an additional condition wherewith such a decomposition is possible.

AMS Subject Classification (1991): 26A15, 42A32

Keyword(s): uniform convergence, monotone sequences

Received May 30, 2012. (Registered under 43/2012.)