Theorems · Theorem · measure theory

MeasureTheory.Integrable.mul_prod

∀ {α : Type u_1} {β : Type u_2} [inst : MeasurableSpace α] [inst_1 : MeasurableSpace β] {μ : MeasureTheory.Measure α}
  {ν : MeasureTheory.Measure β} {L : Type u_4} [inst_2 : NormedRing L] {f : α → L} {g : β → L},
  MeasureTheory.Integrable f μ →
    MeasureTheory.Integrable g ν → MeasureTheory.Integrable (fun z => f z.1 * g z.2) (μ.prod ν)

Defined in

Mathlib.MeasureTheory.Integral.Prod

Cited by

2 results in Mathlib

Foundations

Depth 221 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceMeasurableSpaceNormedRing