ThmDex – An index of mathematical definitions, results, and conjectures.
F10459
Formulation 0
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( \sum_{n \in \mathbb{N}} X_n \right) = \sum_{n \in \mathbb{N}} \mathbb{E}(X_n) \end{equation}