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Dec 22, 2012 at 7:22 comment added Todd Trimble Yes, like Mark, I don't think this is in the intended spirit of the question, which is about sophisticated proofs for facts that have much easier proofs.
Jun 15, 2011 at 15:10 comment added Mark I don't see this as a simple fact. To construct Lebesgue measure you usually have to prove such a statement (or something similar) anyway.
Jun 5, 2011 at 16:54 history answered Bill Johnson CC BY-SA 3.0