Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that
(i) | $X_0, X_1, X_2, \ldots : \Omega \to \mathbb{R}$ are each a D3161: Random real number on $P$ |
(ii) | $X_0, X_1, X_2, \ldots$ is an D2713: Independent random collection on $P$ |
Then $X_0, X_1, X_2, \ldots$ is an D3842: Uncorrelated random collection on $P$.