A note on Furstenberg's filtering problem

Rodolphe Garbit (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

This short note gives a positive answer to an old question in elementary probability theory that arose in Furstenberg's seminal article "Disjointness in Ergodic Theory." As a consequence, Furstenberg's filtering theorem holds without any integrability assumption.

Domaines: Probabilités [math.PR]; Systèmes dynamiques [math.DS]

Rodolphe Garbit. A note on Furstenberg's filtering problem. Israel Journal of Mathematics, 2011, 182 (1), pp.333-336. ⟨10.1007/s11856-011-0033-5⟩. ⟨hal-00387100v3⟩