Theorems · Theorem · measure theory

MeasureTheory.Measure.isMulLeftInvariant_eq_smul

∀ {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] [SecondCountableTopology G]
  (μ' μ : MeasureTheory.Measure G) [inst_7 : μ.IsHaarMeasure] [inst_8 : MeasureTheory.IsFiniteMeasureOnCompacts μ']
  [inst_9 : μ'.IsMulLeftInvariant], μ' = μ'.haarScalarFactor μ • μ

Uniqueness of left-invariant measures: Two Haar measures coincide up to a multiplicative constant in a second countable group.

Defined in

Mathlib.MeasureTheory.Measure.Haar.Unique

Cited by

1 results in Mathlib

Foundations

Depth 279 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceGroupIsTopologicalGroupMeasurableSpaceBorelSpaceLocallyCompactSpaceSecondCountableTopologyMeasureTheory.Measure.IsHaarMeasureMeasureTheory.IsFiniteMeasureOnCompactsMeasureTheory.Measure.IsMulLeftInvariant