Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that
| (i) | $X_j : \Omega \to \mathbb{R}$ is a D3161: Random real number on $P$ for each $j \in J$ |
| (ii) | $\{ X_j \}_{j \in J}$ is an D2713: Independent random collection on $P$ |
Then $\{ X_j \}_{j \in J}$ is an D3842: Uncorrelated random collection on $P$.