Theorems · Theorem · measure theory

ContinuousMapZero.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 : Zero ↑t]
  [inst_5 : TopologicalSpace X] [OpensMeasurableSpace X] [SecondCountableTopologyEither X C(↑t, E)],
  MeasurableSet s →
    ∀ (f : X → Y → E) (g : ContinuousMapZero (↑t) E),
      ContinuousOn (Function.uncurry f) (s ×ˢ t) →
        (∀ᵐ (x : X) ∂μ.restrict s, f x ↑0 = 0) →
          MeasureTheory.AEStronglyMeasurable (fun x => ContinuousMapZero.mkD (t.domRestrict (f x)) g) (μ.restrict s)

Defined in

Mathlib.MeasureTheory.SpecificCodomains.ContinuousMapZero

Cited by

2 results in Mathlib

Foundations

Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceTopologicalSpaceNormedAddCommGroupCompactSpaceZeroTopologicalSpaceOpensMeasurableSpaceSecondCountableTopologyEither