# Monotone convergence vs Dominated Convergence

• August 20th 2011, 04:40 AM
TheProphet
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, $\lim_{n \to \infty} \mathbb{E}[X_{n}] = \mathbb{E}[X]$ ?
• August 20th 2011, 09:11 AM
girdav
Re: Monotone convergence vs Dominated Convergence
If $\{X_n\}$ converges almost everywhere to $X$, yes.