Theorems · Theorem · measure theory

MeasureTheory.integral_integral_symm

∀ {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 = ∫ (z : β × α), f z.2 z.1 ∂ν.prod μ

Reversed version of Fubini's Theorem (symmetric version).

Defined in

Mathlib.MeasureTheory.Integral.Prod

Cited by

0 results in Mathlib

Foundations

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

Assumes

MeasurableSpaceMeasurableSpaceNormedAddCommGroupMeasureTheory.SFiniteNormedSpaceMeasureTheory.SFinite