Theorems · Theorem · Lie groups

MeasureTheory.Measure.isAddHaarMeasure_map

∀ {G : Type u_1} [inst : MeasurableSpace G] [inst_1 : AddGroup G] [inst_2 : TopologicalSpace G]
  (μ : MeasureTheory.Measure G) [μ.IsAddHaarMeasure] [BorelSpace G] [ContinuousAdd G] {H : Type u_3}
  [inst_6 : AddGroup H] [inst_7 : TopologicalSpace H] [inst_8 : MeasurableSpace H] [BorelSpace H]
  [IsTopologicalAddGroup H] (f : G →+ H),
  Continuous ⇑f →
    Function.Surjective ⇑f →
      Filter.Tendsto (⇑f) (Filter.cocompact G) (Filter.cocompact H) →
        (MeasureTheory.Measure.map (⇑f) μ).IsAddHaarMeasure

The image of an additive Haar measure under a continuous surjective proper additive group homomorphism is again an additive Haar measure. See also AddEquiv.isAddHaarMeasure_map, ContinuousAddEquiv.isAddHaarMeasure_map and ContinuousLinearEquiv.isAddHaarMeasure_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

MeasurableSpaceAddGroupTopologicalSpaceMeasureTheory.Measure.IsAddHaarMeasureBorelSpaceContinuousAddAddGroupTopologicalSpaceMeasurableSpaceBorelSpaceIsTopologicalAddGroup