Suppose X is a compact subset of Euclidean Space. Let P(X) be the set of all Borel probability measures on X. Now let's consider the set of all Borel probability measures on X with finite support. My question is: is this subset compact? Or consider the set of all Borel probability measures on X with the cardinality of the support bounded above by some fix number K. Then is this set compact?
2026-03-28 05:22:42.1774675362
Are the set of finitely supported probability measure in Euclidean space compact?
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