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Results tagged with lebesgue-measure
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user 166207
3
votes
1
answer
404
views
To show a set is a set of positive Lebesgue measure in $ \mathbb{R}$
Let $E\subset \mathbb{R}$ be a set of positive Lebesgue measure. Can we find $l>0$ such that $$\bigcap_{-l\leq t \leq l}t+E$$ is a set of positive Lebesgue measure?
Notation: $t+E=\{t+e|e\in E\}$
- 173
13
votes
1
answer
551
views
Regarding a positive Lebesgue measure set in $\mathbb{R}^2$
Let $P\subset \mathbb{R}^2$ be a positive Lebesgue measure set. Then $P$ does not necessarily contain a subset of the form $A\times B$ where $A,B\subset \mathbb{R}$ are of positive Lebesgue measure.
F …
- 173