Is it possible to exchange a sum in a conditional expectation

Question

Let $X_1, X_2, \ldots \geqslant 0$ and $Y$ be RVs over $\mathbb{R}^n$. Then is it true that $\mathbf{E} \left[ \sum_{i = 1}^{\infty} X_i \mid Y \right] = \sum_{i = 1}^{\infty} \mathbf{E} [X_i \mid Y]$? I know this is true for non-conditional expectations.