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7 votes
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Comparison of several topologies for probability measures

Let $X$ be a compact metric space and denote $\mathcal M(X)$ the set of probability measures on $X$. For $\mu\in\mathcal M(X)$ we write $\operatorname{supp} \mu$ for the support of $\mu$. As is well ...
Kass's user avatar
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2 votes
1 answer
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Complex Borel measures: does $\mu_n \to \mu$ weakly imply $|\mu|(\Theta) \le \liminf_n |\mu_n|(\Theta)$ for every open subset $\Theta$?

Let $\Omega$ be a metric space, $C_b(\Omega)$ the space of all real-valued bounded continuous functions on $\Omega$, and $\mathcal{M}(\Omega)$ the space of all finite signed Borel measures on $\Omega$...
Analyst's user avatar
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