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Theorems · Definition · measure theory

MeasureTheory.Measure.haar

{G : Type u_1} →
  [inst : Group G] →
    [inst_1 : TopologicalSpace G] →
      [IsTopologicalGroup G] →
        [inst : MeasurableSpace G] → [BorelSpace G] → [LocallyCompactSpace G] → MeasureTheory.Measure G

haar is some choice of a Haar measure, on a locally compact group.

Defined in
Mathlib.MeasureTheory.Measure.Haar.Basic
Cited by
11 results in Mathlib
Foundations
Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
GroupTopologicalSpaceIsTopologicalGroupMeasurableSpaceBorelSpaceLocallyCompactSpace

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MeasureTheory.mulEquivHaarChar · cited by 12MeasureTheory.mulEquivHaa…MeasureTheory.Measure.modularCharacterFun · cited by 5Measure.modularCharacterF…MeasureTheory.Measure.modularCharacterFun_eq_haarScalarFactor · cited by 3Measure.modularCharacterF…MeasureTheory.mulEquivHaarChar_eq · cited by 3MeasureTheory.mulEquivHaa…MeasureTheory.Measure.measure_isMulInvariant_eq_smul_of_isCompact_closure_of_measurableSet · cited by 1Measure.measure_isMulInva…MeasureTheory.mulEquivHaarChar_refl · cited by 1MeasureTheory.mulEquivHaa…MeasureTheory.Measure.haar.congr_simp · cited by 0haar.congr_simpMeasureTheory.mulEquivHaarChar_trans · cited by 0MeasureTheory.mulEquivHaa…MeasureTheory.Measure.modularCharacterFun_map_mul · cited by 0Measure.modularCharacterF…MeasureTheory.Measure.modularCharacterFun_map_one · cited by 0Measure.modularCharacterF…MeasureTheory.Measure.modularCharacterFun_pos · cited by 0Measure.modularCharacterF…MonoidHom.exists_nhds_isBounded · cited by 0MonoidHom.exists_nhds_isB…MeasureTheory.mulEquivHaarChar_pos · cited by 0MeasureTheory.mulEquivHaa…TopologicalSpace · cited by 24529TopologicalSpaceMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureGroup · cited by 6238GroupBorelSpace · cited by 1602BorelSpaceIsTopologicalGroup · cited by 469IsTopologicalGroupLocallyCompactSpace · cited by 324LocallyCompactSpaceClassical.arbitrary · cited by 161Classical.arbitraryTopologicalSpace.PositiveCompacts · cited by 112TopologicalSpace.Positive…MeasureTheory.Measure.haarMeasure · cited by 10Measure.haarMeasureMeasure.haarCITED BYCITES

Cites10

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Cited by13

Results whose statement or proof uses this declaration.