Theorems · Theorem · measure theory

MeasureTheory.integral_prod_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),
  ∫ (z : β × α), f z.swap ∂ν.prod μ = ∫ (z : α × β), f z ∂μ.prod ν

Defined in

Mathlib.MeasureTheory.Integral.Prod

Cited by

3 results in Mathlib

Foundations

Depth 257 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceMeasurableSpaceNormedAddCommGroupMeasureTheory.SFiniteNormedSpaceMeasureTheory.SFinite