On weak convergence of measures on Hilbert spaces

Abstract

The concept of weak convergence of measures on topological spaces depends on a topology of the space. In this paper we discuss the relationship between weak convergence of measures on a separable Hilbert space H equipped with w- ∗ and strong topology. Starting from this point we rederive a well-known condition for the weak convergence on H, hoping to shed a new light on this matter.