In probability theory, the Doob–Dynkin lemma, named after Joseph L. Doob and Eugene Dynkin (also known as the factorization lemma), characterizes the situation when one random variable is a function of another by the inclusion of the σ {\displaystyle \sigma } -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 σ {\displaystyle \sigma } -algebra generated by the other.
In probability theory, the Doob–Dynkin lemma, named after Joseph L. Doob and Eugene Dynkin (also known as the factorization lemma), characterizes the situation when one random variable is a function of another by the inclusion of the σ {\displaystyle \sigma } -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 σ {\displaystyle \sigma } -algebra generated by the other.
Source: Wikipedia "Doob–Dynkin lemma" · CC BY-SA 4.0
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