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, $\displaystyle \lim_{n \to \infty} \mathbb{E}[X_{n}] = \mathbb{E}[X] $ ?

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- Aug 20th 2011, 04:40 AMTheProphetMonotone 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, $\displaystyle \lim_{n \to \infty} \mathbb{E}[X_{n}] = \mathbb{E}[X] $ ? - Aug 20th 2011, 09:11 AMgirdavRe: Monotone convergence vs Dominated Convergence
If $\displaystyle \{X_n\}$ converges almost everywhere to $\displaystyle X$, yes.