Theorems · Theorem · measure theory

MeasureTheory.Integrable.smul_prod

∀ {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] {R : Type u_4}
  [inst_3 : NormedRing R] [inst_4 : Module R E] [IsBoundedSMul R E] {f : α → R} {g : β → E},
  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 220 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceMeasurableSpaceNormedAddCommGroupNormedRingModuleIsBoundedSMul