Reverse Fatou lemma
= Reverse Fatou lemma
{c}
{title2=$\limsup_n\mathbb E Y_n\leq\mathbb E\limsup_nY_n$}
If $Y_n$ are <random variables> bounded above by an <integrable function> $Z$, with all relevant expectations well defined, <Fatou's lemma> applied to the nonnegative variables $Z-Y_n$ gives $\limsup_n\mathbb E Y_n\leq\mathbb E\limsup_nY_n$. In particular, bounded <indicator random variables> that tend almost surely to zero have probabilities tending to zero.