Theorems · Theorem · measure theory

MeasureTheory.Measure.measure_isHaarMeasure_eq_smul_of_isOpen

∀ {G : Type u_1} [inst : TopologicalSpace G] [inst_1 : Group G] [inst_2 : IsTopologicalGroup G]
  [inst_3 : MeasurableSpace G] [inst_4 : BorelSpace G] [LocallyCompactSpace G] (μ' μ : MeasureTheory.Measure G)
  [inst_6 : μ.IsHaarMeasure] [inst_7 : μ'.IsHaarMeasure] {s : Set G}, IsOpen s → μ' s = μ'.haarScalarFactor μ • μ s

Uniqueness of Haar measures: Given two Haar measures, they coincide in the following sense: they give the same value to open sets, up to the multiplicative constant haarScalarFactor μ' μ.

Defined in

Mathlib.MeasureTheory.Measure.Haar.Unique

Cited by

0 results in Mathlib

Foundations

Depth 278 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceGroupIsTopologicalGroupMeasurableSpaceBorelSpaceLocallyCompactSpaceMeasureTheory.Measure.IsHaarMeasureMeasureTheory.Measure.IsHaarMeasure