Talk:Pre-measure

Countable additivity?

How about countable additivity, isn't that forgotten? -- 20:28, 6 November 2009‎ User:82.168.4.18

hyphen or no hyphen?

premeasure or pre-measure? We should stick with one and run with it. Kevmitch (talk) 06:11, 17 November 2009 (UTC)[reply]

Set difference?

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)[reply]

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)[reply]