I hope some of you can help me out a little.
I read the following in a article, like it's an obvious fact. (http://research.microsoft.com/en-us/...papers/poi.pdf page 18, lemma 11)
Let be a -algebra on the probability space , and let
be some bounded interval.
Let be the -algebra, generated by the restriction of to . Let . Why does there exist for every some and an event such that . ??
In otherwords, can sufficiently be approximated by . Is this obvious?
Is it because ...(and continuity of the probability measure ?)
Also is claimed that Is this true?
Something general like if , does not hold right?
Really looking forward to your suggestions.