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Questions about abstract measure and Lebesgue integral theory. Also concerns such properties as measurability of maps and sets.

5 votes
1 answer
579 views

Existence of a probability measure with "confined" zero measure sets

Hi, I am struggling with the following question that is tangentially arising from a paper I'm working on. It is not at all essential for the revision but it would be nice to know if there is a pleasa …
Rabee Tourky's user avatar
8 votes
1 answer
878 views

Certain compact subset of $L_1$

Let $(\Omega,\Sigma, \mu)$ be a probability measure and $X$ a Banach space. I am interested in subsets $F\subseteq L_\infty (\mu,X)$ that satisfy these two compactness conditions: $F$ is a norm-com …
Rabee Tourky's user avatar
3 votes
Accepted

Certain compact subset of $L_1$

The answer is that (1) and (2) implies $\star$ (this resolves a nice problem in a game theory paper I'm working on though the final unresolved problem has to do with decomposable Banach spaces, which …
Rabee Tourky's user avatar