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Math Help - Monotone convergence vs Dominated Convergence

  1. #1
    Junior Member TheProphet's Avatar
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    Monotone convergence vs Dominated Convergence

    Convergence of random variables.
    I know the criteria for using Monotone convergence and dominated convergence,
    but is the result the same for both?

    That is,  \lim_{n \to \infty} \mathbb{E}[X_{n}] = \mathbb{E}[X] ?
    Last edited by TheProphet; August 20th 2011 at 05:18 AM.
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  2. #2
    Super Member girdav's Avatar
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    Re: Monotone convergence vs Dominated Convergence

    If \{X_n\} converges almost everywhere to X, yes.
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