Theorems · Theorem · measure theory

MeasureTheory.Measure.isMulLeftInvariant_eq_smul_of_regular

∀ {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'.IsMulLeftInvariant] [μ.Regular] [inst_9 : μ'.Regular],
  μ' = μ'.haarScalarFactor μ • μ

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

Defined in

Mathlib.MeasureTheory.Measure.Haar.Unique

Cited by

3 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceGroupIsTopologicalGroupMeasurableSpaceBorelSpaceLocallyCompactSpaceMeasureTheory.Measure.IsHaarMeasureMeasureTheory.Measure.IsMulLeftInvariantMeasureTheory.Measure.RegularMeasureTheory.Measure.Regular