Abstract. We characterize those positive functions on a Boolean algebra $A$ which can be represented as the variation of a quasi-measure on $A$ with values in an Abelian normed group $G$. We also show that if there exists such a representation, then there is one in which $G$ is an $F^*$-lattice.

AMS Subject Classification (1991): 28B10, 28B05, 28A12, 28A60

Received March 8, 2007, and in revised form January 31, 2008. (Registered under 6006/2009.)