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Results tagged with measure-theory
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user 59219
Questions about abstract measure and Lebesgue integral theory. Also concerns such properties as measurability of maps and sets.
6
votes
Can the integration of integrable sections of a measurable function of two variables ever re...
EDIT: The following only provides a partial answer, since it is not clear at all that the first property of the question ($f(x, \cdot) \in L^1(Y, \mathcal{T}, \nu)$) is fulfilled for the given example …
- 734
7
votes
0
answers
473
views
Characterizing the sum $L^1 + L^\infty + L^{1,\infty} + L^{\infty, 1}$ of iterated Lebesgue ...
For the usual Lebesgue spaces $L^p (\mu)$ ($p \in [1,\infty]$) on a ($\sigma$-finite) measure space $(X,\mu)$, it is well-known that one has the characterization
$$
L^p (\mu) = \left\{f : X \to \Bbb{ …
- 734