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

van Putten, C.; van Schuppen, J. H.

Ann. Probab. 13, 934-945 (1985).

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)

Keywords:

conditional independence relation; independence relation; projection operator; realization problem