Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Convergence of indicator functions for L1 r.v.
  1. Indicator functions (Replies: 2)

  2. Indicator function (Replies: 2)

Loading...