Consider the vector space of signed measures $\{m\}$ on $[0,1]$. Endow it with the weak topology generated by all functionals obtained as integral of a continuous function: $\int_{[0,1]} f dm, f \in C^0[0,1]$. Question: is the set of positive measures $m$ with $m([0,1]) \leq 1$ compact? Thanks for clarifying, Marco.
2026-04-11 11:16:09.1775906169
Compactness of bounded measures with respect to weak topology.
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