Theorems · Theorem · Lie groups

MeasureTheory.Measure.modularCharacterFun_eq_haarScalarFactor

∀ {G : Type u_1} [inst : TopologicalSpace G] [inst_1 : Group G] [inst_2 : IsTopologicalGroup G]
  [inst_3 : LocallyCompactSpace G] [inst_4 : MeasurableSpace G] [inst_5 : BorelSpace G] (μ : MeasureTheory.Measure G)
  [inst_6 : μ.IsHaarMeasure] (g : G),
  MeasureTheory.Measure.modularCharacterFun g = (MeasureTheory.Measure.map (fun x => x * g) μ).haarScalarFactor μ

Independence of modularCharacterFun from the chosen Haar measure.

Defined in

Mathlib.MeasureTheory.Group.ModularCharacter

Cited by

3 results in Mathlib

Foundations

Depth 276 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceGroupIsTopologicalGroupLocallyCompactSpaceMeasurableSpaceBorelSpaceMeasureTheory.Measure.IsHaarMeasure