Sul problema ergodico ristretto

Benvenuti, Pietro

Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali, Série 8, Tome 42 (1967) no. 4, pp. 478-480.

Résumé

For a given stationary process $(X, \mathfrak{A}, m, T_{t})$, let $\mathfrak{B}$ be a sub-field of measurable sets and $\mathfrak{C}$ the sub-field of all invariable sets. The mutual independence of the two sub-fields $\mathfrak{B}$ and $\mathfrak{C}$ is a necessary and sufficient condition for the ergodicity of every random variable $\mathfrak{B}$-measurable and integrable.