Abstract
LetX andY be Hausdorff spaces and denote byM (X) andM (Y) the corresponding spaces of finite and non-negative Borel measures, endowed with the weak topology. A Borel map ϕ:X→Y induces the map $$\tilde \varphi $$ :M (X)→M (Y). We give necessary and sufficient conditions for $$\tilde \varphi $$ to be open. In case of ϕ being a surjection between Suslin spaces, $$\tilde \varphi $$ is open if and only if ϕ is.
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