Theorems · Theorem · measure theory

MeasureTheory.nullMeasurable_image_of_fderivWithin

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [FiniteDimensional ℝ E] {s : Set E}
  {f : E → E} {f' : E → E →L[ℝ] E} [inst_3 : MeasurableSpace E] [BorelSpace E] (μ : MeasureTheory.Measure E)
  [μ.IsAddHaarMeasure],
  MeasureTheory.NullMeasurableSet s μ →
    (∀ x ∈ s, HasFDerivWithinAt f (f' x) s x) → Set.InjOn f s → MeasureTheory.NullMeasurableSet (f '' s) μ

If a function is differentiable and injective on a null measurable set, then the image is null measurable.

Defined in

Mathlib.MeasureTheory.Function.Jacobian

Cited by

0 results in Mathlib

Foundations

Depth 270 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceFiniteDimensionalMeasurableSpaceBorelSpaceMeasureTheory.Measure.IsAddHaarMeasure