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As with conditional expectation, this can be further generalized to conditioning on a sigma algebra <math>\mathcal{F}</math>. In that case the conditional distribution is a function <math>\Omega \times \mathcal{B}(\mathbb{R}) \to [0, 1]</math>:
:<math> \kappa_{Y\mid\mathcal{F}}(\omega, A) = \operatorname E[1_{Y \in A} \mid \mathcal{F}](\omega)</math>
=== Regularity ===
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