Abstract
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.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 8, pp. 1149–1152, August, 1992.
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Shor, A.A., Shor, A.É. Characterization of residual σ-algebras. Ukr Math J 44, 1051–1054 (1992). https://doi.org/10.1007/BF01057132
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DOI: https://doi.org/10.1007/BF01057132