ThmDex – An index of mathematical definitions, results, and conjectures.
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
Measurable map
Random variable
Class of random variables
Collection of random variables
Set of random variables
Random collection
Identically distributed random collection
Stationary random collection
Definition D5254
Stationary random sequence
Formulation 1
A D1721: Random collection $X : \mathbb{N} \to \mathsf{Random}(\Omega \to \Xi)$ is stationary if and only if \begin{equation} \forall \, M \in \mathbb{N} : \forall \, n_1, \ldots, n_M \in \mathbb{N} : \forall \, k \in \mathbb{N} : (X_{n_1}, \ldots, X_{n_M}) \overset{d}{=} (X_{n_1 + k}, \ldots, X_{n_M + k}) \end{equation}
Results
Identically distributed random collection need not be stationary