Theorems · Theorem · measure theory

measurableSet_of_differentiableAt_of_isComplete

∀ (𝕜 : Type u_1) [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] (f : E → F)
  [inst_5 : MeasurableSpace E] [OpensMeasurableSpace E] {K : Set (E →L[𝕜] F)},
  IsComplete K → MeasurableSet {x | DifferentiableAt 𝕜 f x ∧ fderiv 𝕜 f x ∈ K}

The set of differentiability points of a function, with derivative in a given complete set, is Borel-measurable.

Defined in

Mathlib.Analysis.Calculus.FDeriv.Measurable

Cited by

2 results in Mathlib

Foundations

Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceMeasurableSpaceOpensMeasurableSpace