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Nov 24, 2022 at 5:36 comment added Fedor Petrov If you have two measurable sets, $X$ of first type and $Y$ of the second type, you may find two boxes $B_x, B_y=B_x+v$, $v\in \mathbb{R}^2$, of the same size in which $X, Y$ correspondingly occupy more than a half, and consider the set $X\cap (Y-v)$, it has positive measure in $B_x$ by pigeonhole principle.
Nov 24, 2022 at 3:39 history edited Martin Sleziak
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Nov 24, 2022 at 2:53 vote accept user483450
Nov 24, 2022 at 2:48 answer added Saúl RM timeline score: 2
Nov 24, 2022 at 2:19 history asked user483450 CC BY-SA 4.0