Theorems · Theorem · Lie groups

MeasureTheory.Measure.isHaarMeasure_map

∀ {G : Type u_1} [inst : MeasurableSpace G] [inst_1 : Group G] [inst_2 : TopologicalSpace G]
  (μ : MeasureTheory.Measure G) [μ.IsHaarMeasure] [BorelSpace G] [ContinuousMul G] {H : Type u_3} [inst_6 : Group H]
  [inst_7 : TopologicalSpace H] [inst_8 : MeasurableSpace H] [BorelSpace H] [IsTopologicalGroup H] (f : G →* H),
  Continuous ⇑f →
    Function.Surjective ⇑f →
      Filter.Tendsto (⇑f) (Filter.cocompact G) (Filter.cocompact H) → (MeasureTheory.Measure.map (⇑f) μ).IsHaarMeasure

The image of a Haar measure under a continuous surjective proper group homomorphism is again a Haar measure. See also MulEquiv.isHaarMeasure_map and ContinuousMulEquiv.isHaarMeasure_map.

Defined in

Mathlib.MeasureTheory.Group.Measure

Cited by

1 results in Mathlib

Foundations

Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceGroupTopologicalSpaceMeasureTheory.Measure.IsHaarMeasureBorelSpaceContinuousMulGroupTopologicalSpaceMeasurableSpaceBorelSpaceIsTopologicalGroup