Geodesic
Trivial bundles of spaces of probability measures
Sbornik. Mathematics, Tome 57 (1987) no. 2, pp. 485-505

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It is proved that the probability measure functor $P$ carries open mappings $f\colon X\to Y$ of finite-dimensional compact metric spaces with infinite fibers $f^{-1}y$ into $Q$-bundles. If in addition the fibers $f^{-1}y$ do not have isolated points, then it is possible to drop the condition that $X$ be finite-dimensional. Also, necessary and sufficient conditions are given for the mapping $P(f)$ to be a trivial bundle with fiber homeomorphic to a Tychonoff cube in the case of a mapping $f$ onto a dyadic compactum. Bibliography: 27 titles. 
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     author = {V. V. Fedorchuk},
     title = {Trivial bundles of spaces of probability measures},
     journal = {Sbornik. Mathematics},
     pages = {485--505},
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     volume = {57},
     number = {2},
     year = {1987},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1987_57_2_a11/}
}
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V. V. Fedorchuk. Trivial bundles of spaces of probability measures. Sbornik. Mathematics, Tome 57 (1987) no. 2, pp. 485-505. http://geodesic.mathdoc.fr/item/SM_1987_57_2_a11/