Let $\{X_i\}_{i=1}^\infty$ be a sequence of iid integrable random variables. Let $A \in \mathbf{B(\mathbb{R})}$. Does the following result hold (with possibly some more assumptions like $P(X_1 \in A) \neq 0$).
$$ \frac{\sum X_i1_{X_i \in A}}{\sum 1_{X_i\in A}} \rightarrow E[X_1|X_1\in A] \qquad \text{a.e P} $$