Theorems · Theorem · measure theory

MeasureTheory.integral_target_eq_integral_abs_det_fderiv_smul

∀ {E : Type u_1} {F : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [FiniteDimensional ℝ E]
  [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace ℝ F] {f' : E → E →L[ℝ] E} [inst_5 : MeasurableSpace E]
  [BorelSpace E] (μ : MeasureTheory.Measure E) [μ.IsAddHaarMeasure] {f : OpenPartialHomeomorph E E},
  (∀ x ∈ f.source, HasFDerivAt (↑f) (f' x) x) →
    ∀ (g : E → F), ∫ (x : E) in f.target, g x ∂μ = ∫ (x : E) in f.source, |(f' x).det| • g (↑f x) ∂μ

Defined in

Mathlib.MeasureTheory.Function.Jacobian

Cited by

1 results in Mathlib

Foundations

Depth 278 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceFiniteDimensionalNormedAddCommGroupNormedSpaceMeasurableSpaceBorelSpaceMeasureTheory.Measure.IsAddHaarMeasure