Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that

(i)	$X : J \to \mathsf{Random}(\Omega \to \mathbb{R}^D)$ is a D5141: Random euclidean real collection on $P$
(ii)	$\mathcal{G} = \{ \mathcal{G}_j \}_{j \in J}$ is a D3346: Sigma-algebra filtration on $P$
(iii)	$(X, \mathcal{G})$ is a D5710: Euclidean real martingale on $P$

Then \begin{equation} \forall \, i, j \in J : \mathbb{E}(X_i) = \mathbb{E}(X_j) \end{equation}