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[Merged by Bors] - feat(measure_theory/function/conditional_expectation): Conditional expectation of an indicator #14058
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…pectation of an indicator (#14058) The main lemma is this: ```lean lemma condexp_indicator (hf_int : integrable f μ) (hs : measurable_set[m] s) : μ[s.indicator f | m] =ᵐ[μ] s.indicator (μ[f | m]) ``` We also use it to prove that if two sigma algebras are "equal under an event", then the conditional expectations with respect to those two sigma algebras are equal under the same event.
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The main lemma is this:
We also use it to prove that if two sigma algebras are "equal under an event", then the conditional expectations with respect to those two sigma algebras are equal under the same event.