Talk:Negligible set

I don't think the last sentence of the following is correct:

Let X be a measurable space equipped with a measure m, and let a subset of X be negligible if it is m-null. Then the negligible sets form a sigma-ideal. The preceding example is a special case of this using counting measure.

With the counting measure, only the empty set is m-null (i.e. with measure zero). Moreover, a countable subset has the same counting measure as the full set, namely infinity. -- 134.95.128.246

You're right! The correct measure to use assigns 0 to any countable set but infinity to any uncountable set. I don't know a name for this measure, so I'll replace "counting measure" with "a suitable measure". (But if anybody else does know a name for this measure, then please add it in, with a link! ^_^) -- Toby Bartels 14:39, 16 Jul 2004 (UTC)

Every sigma ideal - from a measure; however...

"Let X be measurable space equipped with a measure m, and let a subset of X be negligible if it is m-null. Then the negligible sets form a sigma-ideal." This is OK with me. "Every sigma-ideal on X can be recovered in this way by placing a suitable measure on X." Well, this is right, as far as rather pathologic measures are allowed. But if only finite (or equivalently, sigma-finite) measures are allowed, then the sigma-ideal of all sets of first category, say, on [0,1] is not like that. Boris Tsirelson (talk) 15:59, 30 November 2008 (UTC)