Theorems · Theorem · measure theory

MeasureTheory.Measure.addHaar_image_linearMap

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [inst_2 : MeasurableSpace E] [BorelSpace E]
  [FiniteDimensional ℝ E] (μ : MeasureTheory.Measure E) [μ.IsAddHaarMeasure] (f : E →ₗ[ℝ] E) (s : Set E),
  μ (⇑f '' s) = ENNReal.ofReal |LinearMap.det f| * μ s

The image of a set s under a linear map f has measure equal to μ s times the absolute value of the determinant of f.

Defined in

Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar

Cited by

4 results in Mathlib

Foundations

Depth 258 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceMeasurableSpaceBorelSpaceFiniteDimensionalMeasureTheory.Measure.IsAddHaarMeasure