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Aug 9, 2022 at 7:50 vote accept Keen-ameteur
Aug 7, 2022 at 15:32 answer added alesia timeline score: 2
Aug 7, 2022 at 8:16 comment added Keen-ameteur @mlk When you say this set should have a name, do you mean $A^\epsilon$ or my $A^{(t)}$?
Aug 7, 2022 at 8:15 comment added Keen-ameteur I revised the question and added the condition of being compact, since I was hoping for something more general, but I do not yet how to exclude the dense sets.
Aug 7, 2022 at 8:13 history edited Keen-ameteur CC BY-SA 4.0
Revised the question following suggestions.
Aug 6, 2022 at 22:09 comment added user95282 $A^\varepsilon$ and $A^{(t)}$ cannot distinguish $A$ from its closure, so you may have to assume that $A$ is closed.
Aug 5, 2022 at 17:13 comment added mlk You will definitely need some sufficient notion of niceness, with the obvious standard counterexample being the open, dense sets of arbitrary small measure you can construct as the union of a sequence of smaller and smaller balls around any countable dense set. (Btw, this set should really have a name, since it comes up so often in similar questions...)
Aug 5, 2022 at 14:20 history asked Keen-ameteur CC BY-SA 4.0