On continuous image averaging of probability measures

Sun Man Chang

Vol. 65 (1976), No. 1, 13–17

DOI: 10.2140/pjm.1976.65.13

Abstract

Let M be a compact space, and X a complete sparable metric space. Let P(X) denote the probability measures on X. Let λ be a probability measure on M. Define a function φ_λ from C(M,P(X)) to P(X) by φ_λ(T)(f) = ∫ T(t)(f)dλ(t) for every T ∈ C(M,P(X)), f ∈ C(X). We show that φ_λ is an open mapping.

Mathematical Subject Classification 2000

Primary: 46E27

Milestones

Received: 21 October 1975

Published: 1 July 1976