Any MV-algebra M can be embedded as a lattice in the Boolean algebra B(M) that is R-generated by M . We relate the study of states on an MV-algebra M to the study of finitely additive probabilities on B(M). In particular, we show that each state on M can be uniquely extended to a finitely additive probability on B(M). In case that M is a PMV-algebra, the conditional state s(a|b) defined for a, ...
