Talk:Vitali covering lemma

From Wikipedia, the free encyclopedia

[edit] Infinite version statement

This was previously stated with 3 in place of 5, which was incorrect, as the following example shows. In one dimension, take

Z:=\{B(x,r):|x|<1/2,\,|x|<r<(|x|+1)/3\}.

Then every ball in Z contains 0, and hence every disjoint subcollection of Z consists of just one ball. But for any one ball B\in Z, the expanded ball 3B does not cover \bigcup Z=(-1,1).

One can replace 5 with any number larger than 3 (but not 3), but this does not seem to be worth the effort. Oded (talk) 00:43, 5 May 2008 (UTC)