Solution
= Solution
The <conditional expectation> $\mathbb E[X\mid\mathcal G]$ is the almost surely unique integrable, $\mathcal G$-measurable random variable $Z$ such that $\int_AZ\,d\mathbb P=\int_AX\,d\mathbb P$ for every $A\in\mathcal G$.
= Solution
The <conditional expectation> $\mathbb E[X\mid\mathcal G]$ is the almost surely unique integrable, $\mathcal G$-measurable random variable $Z$ such that $\int_AZ\,d\mathbb P=\int_AX\,d\mathbb P$ for every $A\in\mathcal G$.