M. Studeny: Multiinformation and the problem of characterization of conditional independence relations. Problems of Control and Information Theory 18 (1989), n. 1, pp. 3-16.

Certain algebraic relation between multiinformation and conditional mutual information is established. It is shown to be applicable to the problem of characterization of conditional independence relations (= structures) arising in connection with probabilistic expert systems. More concretely, a new property (axiom) of these relations is derived. Some auxiliary results have their own significance: the characterization of marginally continous measures and the information-theoretical characterization of the conditional product of measures.

AMS classification 94A15, 94A17, 68T30

stochastic conditional independence
axiomatic characterization
marginally continuous measures

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The paper gives an answer to an open open question formulated in the book: