Theorems · Theorem · measure theory

MeasureTheory.lintegral_prod_swap

∀ {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] [MeasureTheory.SFinite μ] (f : α × β → ENNReal),
  ∫⁻ (z : β × α), f z.swap ∂ν.prod μ = ∫⁻ (z : α × β), f z ∂μ.prod ν

Defined in

Mathlib.MeasureTheory.Measure.Prod

Cited by

2 results in Mathlib

Foundations

Depth 224 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceMeasurableSpaceMeasureTheory.SFiniteMeasureTheory.SFinite