Theorems · Theorem · measure theory

ContinuousMap.aeStronglyMeasurable_restrict_mkD_restrict_of_uncurry

∀ {X : Type u_1} {Y : Type u_2} [inst : MeasurableSpace X] {μ : MeasureTheory.Measure X} [inst_1 : TopologicalSpace Y]
  {E : Type u_3} [inst_2 : NormedAddCommGroup E] {s : Set X} {t : Set Y} [CompactSpace ↑t] [inst_4 : TopologicalSpace X]
  [OpensMeasurableSpace X] [SecondCountableTopologyEither X C(↑t, E)],
  MeasurableSet s →
    ∀ (f : X → Y → E) (g : C(↑t, E)),
      ContinuousOn (Function.uncurry f) (s ×ˢ t) →
        MeasureTheory.AEStronglyMeasurable (fun x => ContinuousMap.mkD (t.domRestrict (f x)) g) (μ.restrict s)

Defined in

Mathlib.MeasureTheory.SpecificCodomains.ContinuousMap

Cited by

3 results in Mathlib

Foundations

Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceTopologicalSpaceNormedAddCommGroupCompactSpaceTopologicalSpaceOpensMeasurableSpaceSecondCountableTopologyEither