Theorems · Theorem · measure theory

MeasureTheory.lintegral_lintegral_add_neg

∀ {G : Type u_1} [inst : MeasurableSpace G] [inst_1 : AddGroup G] [MeasurableAdd₂ G] (μ ν : MeasureTheory.Measure G)
  [MeasureTheory.SFinite ν] [MeasureTheory.SFinite μ] [MeasurableNeg G] [μ.IsAddLeftInvariant] [ν.IsAddLeftInvariant]
  (f : G → G → ENNReal),
  AEMeasurable (Function.uncurry f) (μ.prod ν) →
    ∫⁻ (x : G), ∫⁻ (y : G), f (y + x) (-x) ∂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

MeasurableSpaceAddGroupMeasurableAdd₂MeasureTheory.SFiniteMeasureTheory.SFiniteMeasurableNegMeasureTheory.Measure.IsAddLeftInvariantMeasureTheory.Measure.IsAddLeftInvariant