Theorems · Theorem · measure theory

MeasureTheory.lintegral_lintegral_mul

∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {β : Type u_3} [inst : MeasurableSpace β]
  {ν : MeasureTheory.Measure β} {f : α → ENNReal} {g : β → ENNReal},
  AEMeasurable f μ →
    AEMeasurable g ν → ∫⁻ (x : α), ∫⁻ (y : β), f x * g y ∂ν ∂μ = (∫⁻ (x : α), f x ∂μ) * ∫⁻ (y : β), g y ∂ν

A double integral of a product where each factor contains only one variable is a product of integrals

Defined in

Mathlib.MeasureTheory.Integral.Lebesgue.Add

Cited by

3 results in Mathlib

Foundations

Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpace