Geodesic
On Convex Hulls of Compact Sets of Probability Measures with Countable Supports
Funkcionalʹnyj analiz i ego priloženiâ, Tome 45 (2011) no. 1, pp. 83-88

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E. Michael and I. Namioka proved the following theorem. Let $Y$ be a convex $G_\delta$-subset of a Banach space $E$ such that if $K\subset Y$ is a compact space, then its closed (in $Y$) convex hull is also compact. Then every lower semicontinuous set-valued mapping of a paracompact space $X$ to $Y$ with closed (in $Y$) convex values has a continuous selection. E. Michael asked the question: Is the assumption that $Y$ is $G_\delta$ essential? In this note we give an affirmative answer to this question of Michael.
Keywords: continuous selection, set-valued mapping, lower semicontinuity
Mots-clés : paracompact space. 
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     author = {V. L. Gejnts and V. V. Filippov},
     title = {On {Convex} {Hulls} of {Compact} {Sets} of {Probability} {Measures} with {Countable} {Supports}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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V. L. Gejnts; V. V. Filippov. On Convex Hulls of Compact Sets of Probability Measures with Countable Supports. Funkcionalʹnyj analiz i ego priloženiâ, Tome 45 (2011) no. 1, pp. 83-88. http://geodesic.mathdoc.fr/item/FAA_2011_45_1_a7/