Theorems · Theorem · measure theory

MeasureTheory.Measure.map_addHaar_smul

∀ {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] {r : ℝ},
  r ≠ 0 → MeasureTheory.Measure.map (fun x => r • x) μ = ENNReal.ofReal |(r ^ Module.finrank ℝ E)⁻¹| • μ

Defined in

Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar

Cited by

6 results in Mathlib

Foundations

Depth 255 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceMeasurableSpaceBorelSpaceFiniteDimensionalMeasureTheory.Measure.IsAddHaarMeasure