Theorems · Theorem · real analysis

measurable_lineDeriv

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] [LocallyCompactSpace 𝕜] {E : Type u_2}
  [inst_2 : NormedAddCommGroup E] [inst_3 : NormedSpace 𝕜 E] [inst_4 : MeasurableSpace E] [OpensMeasurableSpace E]
  {F : Type u_3} [inst_6 : NormedAddCommGroup F] [inst_7 : NormedSpace 𝕜 F] [CompleteSpace F] {f : E → F} {v : E}
  [inst_9 : MeasurableSpace F] [BorelSpace F], Continuous f → Measurable fun x => lineDeriv 𝕜 f x v

Defined in

Mathlib.Analysis.Calculus.LineDeriv.Measurable

Cited by

1 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldLocallyCompactSpaceNormedAddCommGroupNormedSpaceMeasurableSpaceOpensMeasurableSpaceNormedAddCommGroupNormedSpaceCompleteSpaceMeasurableSpaceBorelSpace