Theorems · Theorem · measure theory

MeasureTheory.integrable_prod

∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {E : Type u_8} {F : Type u_9}
  [inst : NormedAddCommGroup E] [NormedSpace ℝ E] [inst_2 : NormedAddCommGroup F] [NormedSpace ℝ F] {f : α → E × F},
  MeasureTheory.Integrable f μ ↔
    MeasureTheory.Integrable (fun x => (f x).1) μ ∧ MeasureTheory.Integrable (fun x => (f x).2) μ

Defined in

Mathlib.MeasureTheory.Function.L1Space.Integrable

Cited by

0 results in Mathlib

Foundations

Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace