Real Analysis and Prob. question

JuanFangio · February 1st, 2006, 1:53 pm

Hello, finance gurus. Can anyone help me complete these two proofs? Thanks in advance....Suppose An is a sequence of sets in F (sigma-algebra) such that P(An)=1 for all n=1,2,....- Show that P(union from i=1 to infinite of Ai) = 1- Show that P(intersection from i=1 to infinite of Ai) = 1Help, please!!

N · February 1st, 2006, 3:50 pm

I've got a better one.Suppose the members of the set, An form a group.Can you prove Jaun Rangio's assertion cannot be true for a certain type of group?How would you need to constrain the concept of set to make this true? (A little bit topos theory here for the more mathematical quants)N

leherbert · February 2nd, 2006, 5:02 pm

1 > Prob(union) > Prob(intersection)For the first part. Now prove the second part Show that An\(union Ai, i<n) has probability 0.Then use sigma additivity.