Theorems · Theorem · measure theory

aemeasurable_deriv_with_param

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {F : Type u_3} [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] {α : Type u_4} [inst_3 : TopologicalSpace α] [inst_4 : MeasurableSpace α]
  [OpensMeasurableSpace α] [CompleteSpace F] [LocallyCompactSpace 𝕜] [inst_8 : MeasurableSpace 𝕜]
  [OpensMeasurableSpace 𝕜] [inst_10 : MeasurableSpace F] [BorelSpace F] {f : α → 𝕜 → F},
  Continuous (Function.uncurry f) → ∀ (μ : MeasureTheory.Measure (α × 𝕜)), AEMeasurable (fun p => deriv (f p.1) p.2) μ

Defined in

Mathlib.Analysis.Calculus.FDeriv.Measurable

Cited by

0 results in Mathlib

Foundations

Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceMeasurableSpaceOpensMeasurableSpaceCompleteSpaceLocallyCompactSpaceMeasurableSpaceOpensMeasurableSpaceMeasurableSpaceBorelSpace