Theorems · Theorem · measure theory

MeasureTheory.integral_comap_eq_mulEquivHaarChar_smul

∀ {G : Type u_1} [inst : Group G] [inst_1 : TopologicalSpace G] [inst_2 : MeasurableSpace G] [inst_3 : BorelSpace G]
  [inst_4 : IsTopologicalGroup G] [inst_5 : LocallyCompactSpace G] (μ : MeasureTheory.Measure G) [μ.IsHaarMeasure]
  [μ.Regular] {f : G → ℝ} (φ : G ≃ₜ* G),
  ∫ (a : G), f a ∂MeasureTheory.Measure.comap (⇑φ) μ = MeasureTheory.mulEquivHaarChar φ • ∫ (a : G), f a ∂μ

Defined in

Mathlib.MeasureTheory.Measure.Haar.MulEquivHaarChar

Cited by

0 results in Mathlib

Foundations

Depth 282 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupTopologicalSpaceMeasurableSpaceBorelSpaceIsTopologicalGroupLocallyCompactSpaceMeasureTheory.Measure.IsHaarMeasureMeasureTheory.Measure.Regular