= Closed uniformly tight compactness criterion
A weakly closed <uniformly tight> family of Borel <probability measures> on a <Polish space> is weakly compact. Embed the underlying space into a compact <metric> closure, take subsequential pushforward limits, and use the closed-set <Portmanteau theorem> on the common tightness compact sets. The limit retains full mass in the original space; inverse continuity of the <probability pushforward embedding theorem> then returns the weak limit.
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