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Questions related to various forms of integration including the Riemann integral, Lebesgue integral, Riemann–Stieltjes integral, double integrals, line integrals, contour integrals, surface integrals, integrals of differential forms, ...

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 …
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