Theorems · Theorem · measure theory

MeasureTheory.lintegral_prod_mul

∀ {α : Type u_1} {β : Type u_2} [inst : MeasurableSpace α] [inst_1 : MeasurableSpace β] {μ : MeasureTheory.Measure α}
  {ν : MeasureTheory.Measure β} [MeasureTheory.SFinite ν] {f : α → ENNReal} {g : β → ENNReal},
  AEMeasurable f μ →
    AEMeasurable g ν → ∫⁻ (z : α × β), f z.1 * g z.2 ∂μ.prod ν = (∫⁻ (x : α), f x ∂μ) * ∫⁻ (y : β), g y ∂ν

Defined in

Mathlib.MeasureTheory.Measure.Prod

Cited by

1 results in Mathlib

Foundations

Depth 219 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceMeasurableSpaceMeasureTheory.SFinite