Let $(\Omega,\mathcal{F},\mathbb{P})$ be a probability space and $$ X: \Omega \rightarrow \mathbb{R} $$ is a real-valued random variable.
Let $\mathcal{B}$ a sub-$\sigma $ algebra of $\mathcal{F} $.
What conditions must $X$ fulfill for conditional expectation $\mathbb {E} [X|\mathcal{B} ]$ to exist ?