Formulation on R4567: Countable indicator partition of a random euclidean real number
F10610
Formulation 0
Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that
 (i) $X : \Omega \to \mathbb{R}^D$ is a D4383: Random Euclidean real number on $P$ (ii) $E_0, E_1, E_2, \ldots \in \mathcal{F}$ are each an D1716: Event in $P$ (iii) $E_0, E_1, E_2, \ldots$ is a D5143: Set partition of $\Omega$
Then $$X = \sum_{n = 0}^{\infty} X I_{E_n}$$