Talk:Steinhaus theorem

Latest comment: 5 months ago by 169.234.53.165 in topic The current proof does not work

Untitled edit

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)Reply

"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)Reply

The current proof does not work edit

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  : it needs to be an open interval containing   and which measure is less than twice the measure of   (since  ). But such an interval cannot exist if the convex hull of   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)Reply

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