Characterization of residual σ-algebras - Shor , A. A.; Shor , A. E. (Ukrains’kyi Matematychnyi Zhurnal, 1992)
The behavior of residual σ-algebras is studied. For a probability space (Ω, F, P) a new topology is introduced on the set F of all σ-subalgebras. Necessary and sufficient conditions for the independence of events from the final σ-algebra are obtained in terms of mixing.