Theorems · Theorem · measure theory

MeasureTheory.Measure.addHaarMeasure_eq_iff

∀ {G : Type u_1} [inst : AddGroup G] [inst_1 : TopologicalSpace G] [inst_2 : IsTopologicalAddGroup G]
  [inst_3 : MeasurableSpace G] [inst_4 : BorelSpace G] [SecondCountableTopology G]
  (K₀ : TopologicalSpace.PositiveCompacts G) (μ : MeasureTheory.Measure G) [MeasureTheory.SigmaFinite μ]
  [μ.IsAddLeftInvariant], MeasureTheory.Measure.addHaarMeasure K₀ = μ ↔ μ ↑K₀ = 1

Let μ be a σ-finite left invariant measure on G. Then μ is equal to the additive Haar measure defined by K₀ iff μ K₀ = 1.

Defined in

Mathlib.MeasureTheory.Measure.Haar.Basic

Cited by

1 results in Mathlib

Foundations

Depth 235 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddGroupTopologicalSpaceIsTopologicalAddGroupMeasurableSpaceBorelSpaceSecondCountableTopologyMeasureTheory.SigmaFiniteMeasureTheory.Measure.IsAddLeftInvariant