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Timeline for Intersection of IID fractal sets

Current License: CC BY-SA 4.0

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Jul 18 at 13:18 vote accept Focus
Jul 17 at 20:34 answer added Anthony Quas timeline score: 3
Jul 17 at 11:49 history edited Focus CC BY-SA 4.0
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Jul 17 at 11:49 comment added Focus @unwissen Yes, we may assume that they are closed, thanks.
Jul 17 at 10:12 comment added unwissen @Focus Do you assume $A, B$ to be closed or not? I think that may make a difference. Also, could it be that the question is actually more or less "Are there uncountably many disjoint measurable (, ...) subsets of $[0, 1]$ such that everyone of them has Hausdorff dimension $d > 1/2$"? If this is the case, maybe set theorists/logicians know this.
Jul 16 at 17:30 comment added Focus @AnthonyQuas I mean $A$, $B$ are random subsets of $\mathbb R$, independent, and have the same law.
Jul 16 at 17:02 comment added Anthony Quas What do you mean by IID random subset? See the Furstenberg Intersection Conjecture, for a result in this general direction.
Jul 16 at 16:25 history edited Focus CC BY-SA 4.0
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Jul 16 at 15:06 history asked Focus CC BY-SA 4.0