Theorems · Theorem · measure theory

MeasureTheory.integrable_smul_const

∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {𝕜 : Type u_8} [inst : NontriviallyNormedField 𝕜]
  [CompleteSpace 𝕜] {E : Type u_9} [inst_2 : NormedAddCommGroup E] [inst_3 : NormedSpace 𝕜 E] {f : α → 𝕜} {c : E},
  c ≠ 0 → (MeasureTheory.Integrable (fun x => f x • c) μ ↔ MeasureTheory.Integrable f μ)

Defined in

Mathlib.MeasureTheory.Function.L1Space.Integrable

Cited by

1 results in Mathlib

Foundations

Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldCompleteSpaceNormedAddCommGroupNormedSpace