Theorems · Theorem · measure theory

MeasureTheory.lintegral_lintegral_mul_inv

∀ {G : Type u_1} [inst : MeasurableSpace G] [inst_1 : Group G] [MeasurableMul₂ G] (μ ν : MeasureTheory.Measure G)
  [MeasureTheory.SFinite ν] [MeasureTheory.SFinite μ] [MeasurableInv G] [μ.IsMulLeftInvariant] [ν.IsMulLeftInvariant]
  (f : G → G → ENNReal),
  AEMeasurable (Function.uncurry f) (μ.prod ν) →
    ∫⁻ (x : G), ∫⁻ (y : G), f (y * x) x⁻¹ ∂ν ∂μ = ∫⁻ (x : G), ∫⁻ (y : G), f x y ∂ν ∂μ

Defined in

Mathlib.MeasureTheory.Group.Prod

Cited by

1 results in Mathlib

Foundations

Depth 226 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceGroupMeasurableMul₂MeasureTheory.SFiniteMeasureTheory.SFiniteMeasurableInvMeasureTheory.Measure.IsMulLeftInvariantMeasureTheory.Measure.IsMulLeftInvariant