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    Sequence of Events

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    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.)

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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 ...

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