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I'm fairly certain the 3 should be raised to the power of the dimension. —Preceding unsigned comment added by 128.208.116.167 ( talk) 03:53, 12 January 2010 (UTC)
The unsigned comment is incorrect. When making such an assertion one should give a reason (first of all, what is wrong with the provided proof?). This lemma applies to arbitrary metric spaces irrespective of any notion of dimension. 68.121.170.218 ( talk) 07:33, 14 January 2010 (UTC)
This was previously stated with 3 in place of 5, which was incorrect, as the following example shows. In one dimension, take
Then every ball in contains , and hence every disjoint subcollection of consists of just one ball. But for any one ball , the expanded ball does not cover .
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)
In the statement of the theorem, I added that the sets in the Vitali class are closed, because it is so in the Falconer reference, and because no other reference or proof is given; anyway a minimal regularity should be assumed I suppose. Bdmy ( talk) 11:44, 14 October 2008 (UTC)
Also, I found disturbing that the celebrated Vitali covering theorem was given in the present article only in terms of the Hausdorff measure, a notion that even professional mathematicians are not necessarily familiar with. So I added a corollary using the Lebesgue measure. Bdmy ( talk) 10:52, 16 October 2008 (UTC)
In the same vein, I found wrong that an article about Vitali's theorem did not indicate what Vitali actually proved. Bdmy ( talk) 13:06, 20 October 2008 (UTC)
The present structure is very awkward. It seems that Vitali covering theorem should be an article on its own. Arcfrk ( talk) 04:39, 26 January 2009 (UTC)
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I'm fairly certain the 3 should be raised to the power of the dimension. —Preceding unsigned comment added by 128.208.116.167 ( talk) 03:53, 12 January 2010 (UTC)
The unsigned comment is incorrect. When making such an assertion one should give a reason (first of all, what is wrong with the provided proof?). This lemma applies to arbitrary metric spaces irrespective of any notion of dimension. 68.121.170.218 ( talk) 07:33, 14 January 2010 (UTC)
This was previously stated with 3 in place of 5, which was incorrect, as the following example shows. In one dimension, take
Then every ball in contains , and hence every disjoint subcollection of consists of just one ball. But for any one ball , the expanded ball does not cover .
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)
In the statement of the theorem, I added that the sets in the Vitali class are closed, because it is so in the Falconer reference, and because no other reference or proof is given; anyway a minimal regularity should be assumed I suppose. Bdmy ( talk) 11:44, 14 October 2008 (UTC)
Also, I found disturbing that the celebrated Vitali covering theorem was given in the present article only in terms of the Hausdorff measure, a notion that even professional mathematicians are not necessarily familiar with. So I added a corollary using the Lebesgue measure. Bdmy ( talk) 10:52, 16 October 2008 (UTC)
In the same vein, I found wrong that an article about Vitali's theorem did not indicate what Vitali actually proved. Bdmy ( talk) 13:06, 20 October 2008 (UTC)
The present structure is very awkward. It seems that Vitali covering theorem should be an article on its own. Arcfrk ( talk) 04:39, 26 January 2009 (UTC)