▾ Set of symbols
▾ Alphabet
▾ Deduction system
▾ Theory
▾ Zermelo-Fraenkel set theory
▾ Set
▾ Subset
▾ Power set
▾ Hyperpower set sequence
▾ Hyperpower set
▾ Hypersubset
▾ Subset algebra
▾ Subset structure
▾ Measurable space
▾ Measure space
▾ Measure-preserving endomorphism
▾ Measure-preserving system
▾ Probability-preserving system
Probability-preserving random euclidean real sequence
Formulation 0
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}