Theorems · Theorem · measure theory

MeasureTheory.Measure.isAddLeftInvariant_eq_smul

∀ {G : Type u_1} [inst : TopologicalSpace G] [inst_1 : AddGroup G] [inst_2 : IsTopologicalAddGroup G]
  [inst_3 : MeasurableSpace G] [inst_4 : BorelSpace G] [LocallyCompactSpace G] [SecondCountableTopology G]
  (μ' μ : MeasureTheory.Measure G) [inst_7 : μ.IsAddHaarMeasure] [inst_8 : MeasureTheory.IsFiniteMeasureOnCompacts μ']
  [inst_9 : μ'.IsAddLeftInvariant], μ' = μ'.addHaarScalarFactor μ • μ

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

Defined in

Mathlib.MeasureTheory.Measure.Haar.Unique

Cited by

8 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceAddGroupIsTopologicalAddGroupMeasurableSpaceBorelSpaceLocallyCompactSpaceSecondCountableTopologyMeasureTheory.Measure.IsAddHaarMeasureMeasureTheory.IsFiniteMeasureOnCompactsMeasureTheory.Measure.IsAddLeftInvariant