Given a sigma field $\mathfrak{g}$ and a random variable $X$. A conditional expectation of $X$ is defined as $E(X|\mathfrak{g})$ and this conditional expectation is $\mathfrak{g}$ measurable.Now define an indicator function $\mathfrak{1}_G$ where $G\in\mathfrak{g}$. Consider the expression $E(X|\mathfrak{g})\cdot1_G$. If I have an element $l\in\mathfrak{g}$ and $l\not\subseteq G$, then the expression $(E(X|\mathfrak{g})\cdot1_G)(l)$ means $E(X|l)\cdot0$. Am I correct on this?
edit: changed $E(X|\mathfrak{g})\cdot1_G(l)$ to $(E(X|\mathfrak{g})\cdot1_G)(l)$
clarifying:
$(E(X|\mathfrak{g})\cdot1_G)(l)$
the $\cdot$ notation here means multiplication
Since $E(X \mid \mathfrak{g})$ is a $\mathfrak{g}$-random variable, I think it would be better to write $$(E(X \mid \mathfrak{g}) \cdot 1_G)(l) = E(X \mid \mathfrak{g})(l) \cdot 0.$$ As far as I know, something like "$E(X \mid l)$" is not defined.