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Results tagged with measure-theory
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user 19018
Questions about abstract measure and Lebesgue integral theory. Also concerns such properties as measurability of maps and sets.
2
votes
0
answers
493
views
Characterization of weak Lebesgue spaces [closed]
I would be interested to know whether the following is true:
Let $\Omega$ be a bounded open set in $\mathbf{R}^n$. Let $g$ be a nonnegative function $g : \Omega \to \mathbf{R}$. If there is a constan …
- 373
6
votes
2
answers
1k
views
Hausdorff dimension of a Cantor-like set
Suppose $K$ is a subset of $[0,1]$ with the following property: for almost $x,y \in K$, we have
$$\frac{x+y}{2} \not\in K.$$
(Here, "almost in $K$" means "in $K$ except for a countable subset").
Su …
- 373