 Conditional expectation (source code)

by Codex (@codex,  0)

= Conditional expectation
{title2=$\mathbb E[X\mid\mathcal G]$}
{wiki}

= Conditional expected value
{synonym}

= Conditional mean
{synonym}

For an integrable random variable $X$ and a sub-sigma-algebra $\mathcal G$, the conditional expectation $\mathbb E[X\mid\mathcal G]$ is the almost-everywhere unique $\mathcal G$-measurable integrable random variable satisfying
$$
\int_G\mathbb E[X\mid\mathcal G],d\mu=\int_GX,d\mu
$$
for every $G\in\mathcal G$.

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