Theorems · Theorem · measure theory

MeasureTheory.distribHaarChar_eq_of_measure_smul_eq_mul

∀ {G : Type u_1} {A : Type u_2} [inst : Group G] [inst_1 : AddCommGroup A] [inst_2 : DistribMulAction G A]
  [inst_3 : TopologicalSpace A] [inst_4 : IsTopologicalAddGroup A] [inst_5 : LocallyCompactSpace A]
  [inst_6 : ContinuousConstSMul G A] {g : G} [inst_7 : MeasurableSpace A] [BorelSpace A] {μ : MeasureTheory.Measure A}
  [μ.IsAddHaarMeasure] [μ.Regular] {s : Set A},
  μ s ≠ 0 → μ s ≠ ⊤ → ∀ {r : NNReal}, μ (g • s) = ↑r * μ s → (MeasureTheory.distribHaarChar A) g = r

Defined in

Mathlib.MeasureTheory.Measure.Haar.DistribChar

Cited by

0 results in Mathlib

Foundations

Depth 281 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupAddCommGroupDistribMulActionTopologicalSpaceIsTopologicalAddGroupLocallyCompactSpaceContinuousConstSMulMeasurableSpaceBorelSpaceMeasureTheory.Measure.IsAddHaarMeasureMeasureTheory.Measure.Regular