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Results tagged with measure-theory
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user 43954
Questions about abstract measure and Lebesgue integral theory. Also concerns such properties as measurability of maps and sets.
2
votes
Non-measurable sets on groups from translation invariance
For any infinite group $G$ we can easily construct a Vitali subset $V$ of $G$. Indeed, pick an arbitrary countable infinite subgroup $H$ of $G$ and let $V$ be a subset of $G$ which intersects each rig …
- 5,409
6
votes
If the Hausforff dimension of the graph of a function $u$ is $N$ and $\tilde u = u$ a.e. the...
Put $N=1$, $M=2$, $\Omega=\Bbb R^N$, and $u(x)=(x,0)$ for each $x\in\Bbb R^N$. Then the graph of $u$ is a straight line, so it has Hausdorff dimension $1=N$. On the other hand, let $C\subset [0,1]$ be …
- 5,409