Theorems · Theorem · measure theory

MeasureTheory.setIntegral_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] [MeasureTheory.SFinite μ] {L : Type u_5} [inst_4 : RCLike L]
  (f : α → L) (g : β → L) (s : Set α) (t : Set β),
  ∫ (z : α × β) in s ×ˢ t, f z.1 * g z.2 ∂μ.prod ν = (∫ (x : α) in s, f x ∂μ) * ∫ (y : β) in t, g y ∂ν

Defined in

Mathlib.MeasureTheory.Integral.Prod

Cited by

3 results in Mathlib

Foundations

Depth 267 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceMeasurableSpaceMeasureTheory.SFiniteMeasureTheory.SFiniteRCLike