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Convergence of indicator functions for L1 r.v.

  1. Sep 28, 2012 #1
    Hi all,

    I wonder if the following are equivalent.

    1) E(|X|) < infinity

    2) I(|X| > n) goes to 0 as n goes to infinity (I is the indicator function)

    3) P(|X| > n) goes to 0 as n goes to infinity.


    1) => 2) and 2) => 3) are easy to see, please help me to show 2) => 1) and 3) => 2) if they are indeed true. Thanks.
     
  2. jcsd
  3. Sep 28, 2012 #2
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