Vol. 69, No. 1, 1977

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Measures with continuous image law

Sun Man Chang

Vol. 69 (1977), No. 1, 25–36
Abstract

Let M be a topological space, and X a metric space. Let P(X) denote the collection of probability measures on X. Let C(M,X) denote the set of continuous functions from M to X. Let P(X) have the weak topology, and let C(M,X) have the topology of uniform convergence. For a fixed measure μ P(C(M,X)), and a member t M, define a measure on X by

tμ(A) = μ{f ∈ C (M, X ) : f(t) ∈ A}.

In this paper, we consider the following problem: given a continuous function T : M P(X), when is there a measure μ P(C(M,X)) such that T(t) = for all t?

Mathematical Subject Classification 2000
Primary: 28A32, 28A32
Secondary: 46E30
Milestones
Received: 22 January 1976
Revised: 13 October 1976
Published: 1 March 1977
Authors
Sun Man Chang