Theorems · Theorem · measure theory

MeasureTheory.Measure.addHaarScalarFactor_eq_integral_div_of_continuous_nonneg_pos

∀ {G : Type u_1} [inst : TopologicalSpace G] [inst_1 : AddGroup G] [inst_2 : IsTopologicalAddGroup G]
  [inst_3 : MeasurableSpace G] [inst_4 : BorelSpace G] (μ' μ : MeasureTheory.Measure G) [inst_5 : μ.IsAddHaarMeasure]
  [inst_6 : MeasureTheory.IsFiniteMeasureOnCompacts μ'] [inst_7 : μ'.IsAddLeftInvariant] {f : C(G, ℝ)},
  HasCompactSupport ⇑f ∧ 0 ≤ f ∧ f 0 ≠ 0 → ↑(μ'.addHaarScalarFactor μ) = (∫ (x : G), f x ∂μ') / ∫ (x : G), f x ∂μ

Defined in

Mathlib.MeasureTheory.Measure.Haar.Unique

Cited by

4 results in Mathlib

Foundations

Depth 273 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceAddGroupIsTopologicalAddGroupMeasurableSpaceBorelSpaceMeasureTheory.Measure.IsAddHaarMeasureMeasureTheory.IsFiniteMeasureOnCompactsMeasureTheory.Measure.IsAddLeftInvariant