Theorems · Theorem · measure theory

measurableSet_of_differentiableAt_with_param

∀ (𝕜 : Type u_1) [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] [LocallyCompactSpace E] {F : Type u_3} [inst_4 : NormedAddCommGroup F]
  [inst_5 : NormedSpace 𝕜 F] {α : Type u_4} [inst_6 : TopologicalSpace α] {f : α → E → F} [inst_7 : MeasurableSpace α]
  [OpensMeasurableSpace α] [inst_9 : MeasurableSpace E] [OpensMeasurableSpace E] [CompleteSpace F],
  Continuous (Function.uncurry f) → MeasurableSet {p | DifferentiableAt 𝕜 (f p.1) p.2}

The set of differentiability points of a continuous function depending on a parameter taking values in a complete space is Borel-measurable.

Defined in

Mathlib.Analysis.Calculus.FDeriv.Measurable

Cited by

3 results in Mathlib

Foundations

Depth 183 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceLocallyCompactSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceMeasurableSpaceOpensMeasurableSpaceMeasurableSpaceOpensMeasurableSpaceCompleteSpace