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- TL;DR Summary
- Splitting Unit interval into two measurable sets.
Can the unit interval be split into two measurable sets (A and B each measure 1/2), so that for any sub-interval [c,d] the intersections ##A\cap [c,d]## and ##B\cap [c,d]## each measure half the length of [c,d]? I doubt it, but I would like to see a proof, one way or the other.