A GENERALIZATION OF LYAPUNOVS CONVEXITY THEOREM WITH APPLICATIONS IN OPTIMAL STOPPING

Lyapunov proved that the range of n finite measures defined on the sam e sigma-algebra is compact, and if each measure mu(i) also is atomless , then the range is convex. Although both conclusions may fail for mea sures on different sigma-algebras of the same set, they do hold if the sigma-algebras are nested, which is exactly the setting of classical optimal stopping theory.