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 $(Ω, \mathfrak{F}, P)$ a new topology is introduced on the set $\mathfrak{F}$  of all σ-subalgebras. Necessary and sufficient conditions for the independence of events from the final σ-algebra are obtained in terms of mixing.