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Countable additivity? edit
How about countable additivity, isn't that forgotten? -- 20:28, 6 November 2009 User:82.168.4.18
hyphen or no hyphen? edit
premeasure or pre-measure? We should stick with one and run with it. Kevmitch (talk) 06:11, 17 November 2009 (UTC)
Set difference? edit
Something is wrong with the definition. For example, let R be the family of all sets of reals which are either empty or contain 0, and let μ0 be an arbitrary function from R to [0,∞] such that μ0(∅) = 0. Then μ0 is a premeasure according to our definition: σ-additivity holds trivially because there are no disjoint nonempty sets in R. Clearly, it is not true in general that such an μ0 can be extended to an outer measure, for example this is impossible if the function μ0 is non-monotone. It seems to me that one should additionally require R to be closed under set difference to make it work.—Emil J. 16:25, 19 October 2012 (UTC)
- As currently written, the article requires that R be a ring closed under set differences, so this seems to no longer be an issue. However, this could/should be added to the article as an example of why set differences are needed in the definition. 67.198.37.16 (talk) 19:55, 3 October 2020 (UTC)