Vol. 65, No. 1, 1976

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On continuous image averaging of probability measures

Sun Man Chang

Vol. 65 (1976), No. 1, 13–17
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 φλ from C(M,P(X)) to P(X) by φλ(T)(f) = T(t)(f)(t) for every T C(M,P(X)), f C(X). We show that φλ is an open mapping.

Mathematical Subject Classification 2000
Primary: 46E27
Milestones
Received: 21 October 1975
Published: 1 July 1976
Authors
Sun Man Chang