Abstract. We characterize those positive measures which can be represented as the variation of a measure with values in a Banach space $X$. We also show that if there exists such a representation, then there is one with $X=c_0$.

AMS Subject Classification (1991): 28B05, 28A12, 46B15

Received November 28, 2001, and in revised form May 10, 2002. (Registered under 2884/2009.)