Please see the attached file for the fully formatted problems.
Problem 9. Let.... be a sequence of events. ...
..... and the sequence (C) is increasing.....
The sets B and C are denoted by lim sup n->infinity An and lim inf n->infinity An, respectively.
(a) Show that B and C are events.
(b) Show that...
(c) Find .... (This is supposed to be a sequence of real intervals.)
Please see the attached file for the full solution.
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(a) We know ,
By the definition and property of event, that the union of events is also event, and the intersection of events is event too, then since is event, we know B and C are events too.
(b) Since , then by the definition of intersection, for ...
A Sequence of Events is investigated. The solution is detailed and well presented. The solution was given a rating of "5" by the student who originally posted the question.