Theorems · Theorem · measure theory

MeasureTheory.integral_integral_swap

∀ {α : Type u_1} {β : Type u_2} {E : Type u_3} [inst : MeasurableSpace α] [inst_1 : MeasurableSpace β]
  {μ : MeasureTheory.Measure α} {ν : MeasureTheory.Measure β} [inst_2 : NormedAddCommGroup E] [MeasureTheory.SFinite ν]
  [inst_4 : NormedSpace ℝ E] [MeasureTheory.SFinite μ] ⦃f : α → β → E⦄,
  MeasureTheory.Integrable (Function.uncurry f) (μ.prod ν) →
    ∫ (x : α), ∫ (y : β), f x y ∂ν ∂μ = ∫ (y : β), ∫ (x : α), f x y ∂μ ∂ν

Change the order of Bochner integration.

Defined in

Mathlib.MeasureTheory.Integral.Prod

Cited by

6 results in Mathlib

Foundations

Depth 266 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceMeasurableSpaceNormedAddCommGroupMeasureTheory.SFiniteNormedSpaceMeasureTheory.SFinite