Geodesic
Interior points of convex compactа and continuous choice of exact measures
Funkcionalʹnyj analiz i ego priloženiâ, Tome 58 (2024) no. 1, pp. 125-131

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For a metric space $M$ we prove existence of continuous maps $\{M_n\}^{\infty}_{n=1}$ associating to a compact subset $K \subset M$ a probability measure $M_n(K)$ with $\operatorname{supp}(M_n(K)) = K$ in such a way that the set $\{M_n(K)\}^{\infty}_{n=1}$ is dense in the space of probability measures on $K$.
Keywords: Probability measures, exact measures, interior points of convex sets, continuous selections. 
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     author = {Pavel Semenov},
     title = {Interior points of convex compact{\cyra} and continuous choice of exact measures},
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     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2024_58_1_a8/}
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Pavel Semenov. Interior points of convex compactа and continuous choice of exact measures. Funkcionalʹnyj analiz i ego priloženiâ, Tome 58 (2024) no. 1, pp. 125-131. http://geodesic.mathdoc.fr/item/FAA_2024_58_1_a8/