Representation of States on MV-algebras by Probabilities on R-generated Boolean Algebras

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 vertical bar b)defined for a, b is an element of M with s(b) not equal 0 is extended to the classical conditional probability p(a . b vertical bar b) on B(M) of the a-proportion of the event b, given the event b.