Theorems · Theorem · measure theory

ContinuousMapZero.aeStronglyMeasurable_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] {t : Set Y} [CompactSpace ↑t] [inst_4 : Zero ↑t]
  [inst_5 : TopologicalSpace X] [OpensMeasurableSpace X] [SecondCountableTopologyEither X C(↑t, E)] (f : X → Y → E)
  (g : ContinuousMapZero (↑t) E),
  ContinuousOn (Function.uncurry f) (Set.univ ×ˢ t) →
    (∀ᵐ (x : X) ∂μ, f x ↑0 = 0) →
      MeasureTheory.AEStronglyMeasurable (fun x => ContinuousMapZero.mkD (t.domRestrict (f x)) g) μ

Defined in

Mathlib.MeasureTheory.SpecificCodomains.ContinuousMapZero

Cited by

2 results in Mathlib

Foundations

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

Assumes

MeasurableSpaceTopologicalSpaceNormedAddCommGroupCompactSpaceZeroTopologicalSpaceOpensMeasurableSpaceSecondCountableTopologyEither