Characterization of Measures with a Convex Range: A Generalization of Lyapounov's Theorem

摘要

Let mu vector = (mu(sub 1,...,mu(sub n)) be a vector measure on a measurable space (Omega, F prime), such that each mu(sub i) is nonnegative and finite. In the paper, necessary and sufficient conditions on mu vector are stated such that R(mu vector) := ((mu(sub 1)(F),...,mu(sub n)(F)): F is a member of F prime) is convex. The result is a generalization of Lyapounov's theorem.