The convex continuation of probability charges P and Q on (X,A) is the probabilty charge which assigns to B in A the number

• aP(B)+(1-a)Q(B)

a in [0,1].

If P,Q simple => aP(B)+(1-a)Q(B) simple.

If Ps=the set of all simple probability charges on (X,A) Ps is closed under convex continuation.