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Results tagged with measure-theory
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user 24676
Questions about abstract measure and Lebesgue integral theory. Also concerns such properties as measurability of maps and sets.
4
votes
Convex combinations of Bernoulli Measures
Maybe it is good to note that a similar question:
What is the weak-$^*$ closure of the set
$$
D=\{\mu\in\mathcal{M}_\sigma: \mu\text{ is isomorphic to some }\nu\in C\}?
$$
has a dramatically different …
- 1,658
7
votes
1
answer
251
views
Are all quasi-regular points on Polish spaces generic points?
Let $X$ be a Polish space and $T\colon X\to X$ be a continuous map. We say that a point $x\in X$ is quasi-regular if for every bounded continous function $\varphi\colon X\to\mathbb{R}$ the sequence $A …
- 1,658
15
votes
0
answers
3k
views
Weak$^*$ convergence of measures vs. convergence of supports
Let $X$ be a compact metric space and let $\mathcal M(X)$ denote the set of probability measures on $X$. For $\mu\in\mathcal M(X)$ we write $\text{supp} \mu$ for the support of $\mu$. It is easy to se …
- 1,658