Let $P = (\Omega, \mathcal{F}, \mathbb{P}, T)$ be a D2839: Probability-preserving system such that

(i)	$f : \Omega \to \mathbb{R}^D$ is a D5147: Borel-measurable euclidean real function on $P$

The probability-preserving random euclidean real sequence on $P$ is the D1723: Random sequence \begin{equation} X : \mathbb{N} \to \mathsf{Random}(\Omega \to \mathbb{R}^D), \quad X_n : = f \circ T^n \end{equation}