ABSTRACT
Let X be a separable metric space and M(X) a set of probability measures on the Borel subsets of X. Then if M(X) is compact only if for each > 0, there exists a compact K ⊂ X such that μ(K) >1-ϵ∀μ ∈ M(X). To prove this, first observe that since X is separable, for each n = 1,2,..., we have https://www.w3.org/1998/Math/MathML"> X = ∪ r = 1 ∞ S ( n , r ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003363248/1aad030c-3eb0-4f4f-9996-f6b956f3d3b3/content/math16_211_1_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>
