Talk:Steinhaus theorem

Untitled
there are several different proofs. Should I bother? -unsigned
 * Probably not. Proofs are not that important, one should be enough. Oleg Alexandrov (talk) 01:43, 7 June 2007 (UTC)

"a translation-invariant regular measure defined on the Borel sets of the real line": isn't it the same as "the Lebesgue measure" (up to a multiplicative constant)? If so, wouldn't it be much better to say instead "if μ is the Lebesgue measure on the Real line..."?--Manta (talk) 14:29, 18 March 2011 (UTC)

The current proof does not work
The current proof is false as it is. It probably needs just a few modifications to become valid.

The problem comes from the existence of $$\Delta=(a,b)$$: it needs to be an open interval containing $$A$$ and which measure is less than twice the measure of $$A$$ (since $$\alpha >1/2$$). But such an interval cannot exist if the convex hull of $$A$$ has a measure bigger than twice the measure of A (for instance if A is made of two sets far apart from each other). Myvh773 (talk) 17:14, 13 April 2023 (UTC)


 * I believe replacing A by A intersection Delta should solve the issue. 169.234.53.165 (talk) 00:59, 10 November 2023 (UTC)