Theorems · Theorem · measure theory

MeasureTheory.Measure.isMulLeftInvariant_eq_smul_of_innerRegular

∀ {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 : MeasureTheory.IsFiniteMeasureOnCompacts μ'] [inst_8 : μ'.IsMulLeftInvariant]
  [μ.InnerRegular] [μ'.InnerRegular], μ' = μ'.haarScalarFactor μ • μ

Uniqueness of left-invariant measures: Given two left-invariant measures which are finite on compacts and inner regular, they coincide up to a multiplicative constant.

Defined in

Mathlib.MeasureTheory.Measure.Haar.Unique

Cited by

2 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceGroupIsTopologicalGroupMeasurableSpaceBorelSpaceLocallyCompactSpaceMeasureTheory.Measure.IsHaarMeasureMeasureTheory.IsFiniteMeasureOnCompactsMeasureTheory.Measure.IsMulLeftInvariantMeasureTheory.Measure.InnerRegularMeasureTheory.Measure.InnerRegular