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Results tagged with lebesgue-measure
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user 109573
9
votes
If $A, B$ is a non-trivial partition of $S^1$, is it possible that $R_\theta(A) \cap B$ has ...
This question is explored in great generality by Laczkovich in
Laczkovich, Miklós, "Two constructions of Sierpiński and some cardinal invariants of ideals", Real Anal. Exch. 24(1998-99), No. 2, 663-67 …
- 4,316
4
votes
Accepted
Is there a maximal translation-invariant extension of Lebesgue measure?
The answer is no. This is the main result of "Extensions of invariant measures on Euclidean spaces" by Ciesielski and Pelc.
- 4,316
1
vote
Accepted
The existence of a maximal “cross-sectional” filter on the Boolean algebra of measurable sub...
No. Suppose $\mathcal{F}$ is such a filter. Clearly each $X \in \mathcal{F}$ has positive measure intersection with every positive-length interval. Then neither $[0,1/2]$ nor $[1/2, 1]$ are in the fil …
- 4,316