Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that
(i) | $X_0, X_1, X_2, \ldots : \Omega \to [0, \infty]$ are each a D5101: Random unsigned basic number on $P$ |
Then
\begin{equation}
\mathbb{E} \left( \lim_{N \to \infty} \sum_{n = 0}^N X_n \right)
= \lim_{N \to \infty} \sum_{n = 0}^N \mathbb{E}(X_n)
\end{equation}