 Doob–Dynkin lemma

In probability theory, the Doob–Dynkin lemma, named after Joseph L. Doob and Eugene Dynkin, characterizes the situation when one random variable is a function of another by the inclusion of the formula_1-algebras generated by the random variables.The usual statement of the lemma is formulated in terms of one random variable being measurable with respect to the formula_1-algebra generated by the other.