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Theorems · Definition · measure theory

MeasureTheory.Measure.addHaar

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

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

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

Around this declaration

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

ExistsContDiffBumpBase.w · cited by 11ExistsContDiffBumpBase.wMeasureTheory.addEquivAddHaarChar · cited by 11MeasureTheory.addEquivAdd…ExistsContDiffBumpBase.y · cited by 9ExistsContDiffBumpBase.yMeasureTheory.distribHaarChar · cited by 9MeasureTheory.distribHaar…MeasureTheory.Measure.addModularCharacterFun · cited by 5Measure.addModularCharact…ExistsContDiffBumpBase.u_int_pos · cited by 4ExistsContDiffBumpBase.u_…ExistsContDiffBumpBase.w_support · cited by 4ExistsContDiffBumpBase.w_…MeasureTheory.addEquivAddHaarChar_eq · cited by 3MeasureTheory.addEquivAdd…MeasureTheory.Measure.addModularCharacterFun_eq_addHaarScalarFactor · cited by 3Measure.addModularCharact…ExistsContDiffBumpBase.w_def · cited by 2ExistsContDiffBumpBase.w_…ExistsContDiffBumpBase.w_integral · cited by 2ExistsContDiffBumpBase.w_…Besicovitch.card_le_of_separated · cited by 2Besicovitch.card_le_of_se…LinearMap.exists_map_addHaar_eq_smul_addHaar · cited by 1LinearMap.exists_map_addH…LinearMap.exists_map_addHaar_eq_smul_addHaar' · cited by 1LinearMap.exists_map_addH…integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable_aux2 · cited by 1integral_bilinear_hasLine…TopologicalSpace · cited by 24529TopologicalSpaceMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureAddGroup · cited by 4410AddGroupBorelSpace · cited by 1602BorelSpaceIsTopologicalAddGroup · cited by 1394IsTopologicalAddGroupLocallyCompactSpace · cited by 324LocallyCompactSpaceClassical.arbitrary · cited by 161Classical.arbitraryTopologicalSpace.PositiveCompacts · cited by 112TopologicalSpace.Positive…MeasureTheory.Measure.addHaarMeasure · cited by 21Measure.addHaarMeasureMeasure.addHaarCITED BYCITES

Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by31

Results whose statement or proof uses this declaration.