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In "Elements of Bayesian Statistics" (1990), Florens, Mouchart and Rolin describe two basic forms of reduction of a Bayesian experiment: Marginalization and Conditioning (Ch. 1). I don't understand the conditioning reduction and would appreciate an explanation, if possible in measure-theoretic terms. Thanks.

EDIT: I failed to mention that what i'm struggling with is the definition of a regular conditional experiment.

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This question is a duplicate of this one from stats.stackexchange, and has been answered there.

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