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Results tagged with measure-theory
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user 70478
Questions about abstract measure and Lebesgue integral theory. Also concerns such properties as measurability of maps and sets.
-1
votes
Subspaces of $L_p([0,1])$ whose unit ball is compact for the topology of convergence in measure
No, it does not: otherwise, the given closed subspace $V$ would be a subspace of $L^0$ (the space of measurable functions, metrised with the convergence in measure) whose unit ball would be compact, a …
- 179
5
votes
Radon-Nikodym derivatives as limits of ratios
This question has been thoroughly investigated in the literature a while back. For example see most of the book
Hayes, C. A.; Pauc, C. Y., Derivation and martingales, Ergebnisse der Mathematik u …
- 41.1k
1
vote
Approximation of the radon-derivative
Here some references that show that (surprisingly!) the result you stated is wrong if $\liminf$ is replaced by $\limsup$ and $X=\mathbb{R}^2$.
More precisely, if $\nu$ is the Lebesgue measure on the …
- 179