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3 questions
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Let $E$ be Banach, $\mu_n\to\mu$ weakly on a locally compact $X$, and $f \in C_b(X, E)$. Does $\int f\mathrm d\mu_n\to\int f\mathrm d\mu$ in norm?
Let
$X$ be a metric space,
$(E, |\cdot|)$ a Banach space
$\mathcal M(X)$ the space of all finite signed Borel measures on $X$,
$\mathcal C_b(X)$ be the space of real-valued bounded continuous ...
- 835
1
vote
1
answer
61
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Are there some conditions on a metric space $X$ such that these two types of weak converge of finite signed Borel measures on $X$ are related?
Let
$X$ be a metric space,
$\mathcal M(X)$ the space of all finite signed Borel measures on $X$, and
$\mathcal C_b(X)$ be the space of real-valued bounded continuous functions on $X$.
Then $\mathcal ...
- 835
9
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4
answers
4k
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Is the space of Radon measures a Polish space or at least separable?
Background: I work on a SPDE problem where in order to apply Prokhorov's theorem I need that some measure space is Polish space. And additionaly it would be good if that space is Banach space. Earlier ...
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