An open mapping theorem for measures. (English) Zbl 0679.28004
Let X and Y be Hausdorff spaces and denote by M(X) and M(Y) the corresponding spaces of finite and non-negative Borel measures, endowed with the weak topology. A Borel map \(\phi\) : \(X\to Y\) induces the map \({\tilde \phi}\): M(X)\(\to M(Y)\). The author gives necessary and sufficient conditions for \({\tilde \phi}\) to be open.In case of \(\phi\) being a surjection between Suslin spaces, \({\tilde \phi}\) is open if and only if \(\phi\) is. Several examples complete the exposition.
Reviewer: A.Schief
MSC:
28A33 | Spaces of measures, convergence of measures |
28C15 | Set functions and measures on topological spaces (regularity of measures, etc.) |
60B10 | Convergence of probability measures |
References:
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