If $E[Y/G]=X$ Does that mean $E[X/G]=X$?

Question

if $E[Y/G]=X$ can we use conclude that $E[X/G]=X$?? If so, can anyone explain to me why intuitively?

My understanding is that $X$ is a function of $G$ that's why $E[X/G]=E[f(G)/G]=X$

Answer 1

$\mathsf{E}[Y\mid \mathcal{G}]$ is $\mathcal{G}$-measurable by definition, but not necessarily $X$ (unless you explicitly demand that $X$ is a version of $\mathsf{E}[Y\mid \mathcal{G}]$). Nevertheless, $$ \mathsf{E}[X\mid \mathcal{G}]=\mathsf{E}[\mathsf{E}[Y\mid \mathcal{G}]\mid \mathcal{G}]=\mathsf{E}[Y\mid \mathcal{G}]=X \quad\text{a.s.} $$