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Theorems · Definition · measure theory

MeasureTheory.mulEquivHaarChar

{G : Type u_1} →
  [inst : Group G] →
    [inst_1 : TopologicalSpace G] →
      [inst_2 : MeasurableSpace G] →
        [BorelSpace G] → [IsTopologicalGroup G] → [LocallyCompactSpace G] → G ≃ₜ* G → NNReal

If φ : G ≃ₜ* G then mulEquivHaarChar φ is the positive real factor by which φ scales Haar measures on G.

Defined in
Mathlib.MeasureTheory.Measure.Haar.MulEquivHaarChar
Cited by
12 results in Mathlib
Foundations
Depth 271 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
GroupTopologicalSpaceMeasurableSpaceBorelSpaceIsTopologicalGroupLocallyCompactSpace

Around this declaration

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

MeasureTheory.mulEquivHaarChar_smul_map · cited by 3MeasureTheory.mulEquivHaa…MeasureTheory.mulEquivHaarChar_eq · cited by 3MeasureTheory.mulEquivHaa…MeasureTheory.mulEquivHaarChar_smul_integral_map · cited by 1MeasureTheory.mulEquivHaa…MeasureTheory.mulEquivHaarChar.congr_simp · cited by 1mulEquivHaarChar.congr_si…MeasureTheory.mulEquivHaarChar_refl · cited by 1MeasureTheory.mulEquivHaa…MeasureTheory.mulEquivHaarChar_smul_eq_comap · cited by 0MeasureTheory.mulEquivHaa…MeasureTheory.integral_comap_eq_mulEquivHaarChar_smul · cited by 0MeasureTheory.integral_co…MeasureTheory.mulEquivHaarChar_smul_preimage · cited by 0MeasureTheory.mulEquivHaa…MeasureTheory.mulEquivHaarChar_symm · cited by 0MeasureTheory.mulEquivHaa…MeasureTheory.mulEquivHaarChar_trans · cited by 0MeasureTheory.mulEquivHaa…MeasureTheory.mulEquivHaarChar_eq_one_of_compactSpace · cited by 0MeasureTheory.mulEquivHaa…MeasureTheory.mulEquivHaarChar_pos · cited by 0MeasureTheory.mulEquivHaa…DFunLike.coe · cited by 62936DFunLike.coeTopologicalSpace · cited by 24529TopologicalSpaceMeasurableSpace · cited by 13106MeasurableSpaceGroup · cited by 6238GroupNNReal · cited by 4310NNRealBorelSpace · cited by 1602BorelSpaceMeasureTheory.Measure.map · cited by 858Measure.mapIsTopologicalGroup · cited by 469IsTopologicalGroupLocallyCompactSpace · cited by 324LocallyCompactSpaceContinuousMulEquiv · cited by 65ContinuousMulEquivMeasureTheory.Measure.haarScalarFactor · cited by 31Measure.haarScalarFactorMeasureTheory.Measure.haar · cited by 11Measure.haarMeasureTheory.mulEquivHaarCharCITED BYCITES

Cites12

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

Cited by12

Results whose statement or proof uses this declaration.