Wikipedia:Reference desk/Archives/Mathematics/2020 January 14

= January 14 =

prove that for any event in algebra exists an event in the generated sigma
Let c be an algebra, and g the generated sigma algebra of c. prove that for any delta>0 and for any event E in g, exists an event F in c so p(E\F union F\E)<delta. — Preceding unsigned comment added by 77.126.136.204 (talk) 09:50, 14 January 2020 (UTC)
 * Maybe you should clarify what is your function p and what assumption you have (a measure on g? a probability measure?) pm a 10:52, 14 January 2020 (UTC)
 * Also, –Deacon Vorbis (carbon &bull; videos) 13:39, 14 January 2020 (UTC)


 * Gotta say, I can't make any sense of the question. What do you mean by "let c be an algebra"?  Just a family of subsets of some sample space?  What if the sample space has just one point X?  If p is a probability measure then the only possible events are the empty set (probability 0) or {X} (probability 1), so the statement you want to prove is false.  There has to be more to the question. 2601:648:8202:96B0:0:0:0:DF95 (talk) 21:13, 15 January 2020 (UTC)
 * In fact "let c be an algebra" is very clear: it means: "let c be an algebra". However, an algebra is not just a family of subsets. pm a 23:17, 15 January 2020 (UTC)
 * Oh ok, I see some clarification at field of sets. I was not familiar with the terminology. Thanks. 2601:648:8202:96B0:0:0:0:DF95 (talk) 07:08, 16 January 2020 (UTC)