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Invariance properties of the conditional independence relation. (English) Zbl 0576.60002

Defining the notion of the conditional independence relation for a triple of \(\sigma\)-algebras, necessary and sufficient conditions are derived for certain operations on the independence relation. Two other problems of this work were to study the properties of a projection operator for \(\sigma\)-algebras, and to discuss the \(\sigma\)-algebraic realization problem.
Reviewer: I.G.Kalmár

MSC:

60A10 Probabilistic measure theory
60G05 Foundations of stochastic processes
62B05 Sufficient statistics and fields
62B99 Sufficiency and information
93E03 Stochastic systems in control theory (general)
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