Theorems · Theorem · measure theory

Continuous.aemeasurable2

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {δ : Type u_5} [inst : TopologicalSpace α] [inst_1 : MeasurableSpace α]
  [OpensMeasurableSpace α] [inst_3 : TopologicalSpace β] [inst_4 : MeasurableSpace β] [OpensMeasurableSpace β]
  [inst_6 : TopologicalSpace γ] [inst_7 : MeasurableSpace γ] [BorelSpace γ] [inst_9 : MeasurableSpace δ]
  [SecondCountableTopologyEither α β] {f : δ → α} {g : δ → β} {c : α → β → γ} {μ : MeasureTheory.Measure δ},
  (Continuous fun p => c p.1 p.2) → AEMeasurable f μ → AEMeasurable g μ → AEMeasurable (fun a => c (f a) (g a)) μ

Defined in

Mathlib.MeasureTheory.Constructions.BorelSpace.Basic

Cited by

2 results in Mathlib

Foundations

Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceMeasurableSpaceOpensMeasurableSpaceTopologicalSpaceMeasurableSpaceOpensMeasurableSpaceTopologicalSpaceMeasurableSpaceBorelSpaceMeasurableSpaceSecondCountableTopologyEither