Theorems · Theorem · measure theory

MeasureTheory.Measure.haarScalarFactor_eq_integral_div_of_continuous_nonneg_pos

∀ {G : Type u_1} [inst : TopologicalSpace G] [inst_1 : Group G] [inst_2 : IsTopologicalGroup G]
  [inst_3 : MeasurableSpace G] [inst_4 : BorelSpace G] (μ' μ : MeasureTheory.Measure G) [inst_5 : μ.IsHaarMeasure]
  [inst_6 : MeasureTheory.IsFiniteMeasureOnCompacts μ'] [inst_7 : μ'.IsMulLeftInvariant] {f : C(G, ℝ)},
  HasCompactSupport ⇑f ∧ 0 ≤ f ∧ f 1 ≠ 0 → ↑(μ'.haarScalarFactor 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

TopologicalSpaceGroupIsTopologicalGroupMeasurableSpaceBorelSpaceMeasureTheory.Measure.IsHaarMeasureMeasureTheory.IsFiniteMeasureOnCompactsMeasureTheory.Measure.IsMulLeftInvariant