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Results tagged with measure-theory
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user 127871
Questions about abstract measure and Lebesgue integral theory. Also concerns such properties as measurability of maps and sets.
2
votes
Regular Borel measures and the measure of a singleton
Here's a variation on Nate's argument that needs neither compactness of $S$ nor regularity of $\mu$; instead one has to know that the range of an atomless measure is an interval (in fact, it would be …
- 1,848
2
votes
Accepted
An example of a measurable random process with non-measurable integral
The following example is a variant of an example of Sierpinski that Martin Väth told me; it depends on the Continuum Hypothesis. Let $<^*$ be a well-ordering of $[0,1]$. By CH, $\{s: s<^*t\}$ is alway …
- 1,848
2
votes
Accepted
Weak*-convergence of signed measures
The answer is positive if the sequence $(\nu_n)$ is bounded; please see Theorem IV.9.15 in Dunford/Schwartz, vol. 1. PS: I just notice that this was already observed by Christian a couple of minutes a …
- 1,848
3
votes
Reference request for (weak*) metrizability of a bounded space of signed Radon measures on a...
You can cite Lemma 3.102 and Lemma 3.103 in M. Fabian et al., Banach Space Theory, Springer 2011. Probably there are very many sources that contain this result.
- 1,848