Theorems · Theorem · measure theory

MeasureTheory.integrable_fun_smul_iff

∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : NormedAddCommGroup β]
  {𝕜 : Type u_8} [inst_1 : NormedDivisionRing 𝕜] [inst_2 : MulActionWithZero 𝕜 β] [IsBoundedSMul 𝕜 β] {c : 𝕜},
  c ≠ 0 → ∀ (f : α → β), MeasureTheory.Integrable (fun x => c • f x) μ ↔ MeasureTheory.Integrable f μ

Defined in

Mathlib.MeasureTheory.Function.L1Space.Integrable

Cited by

1 results in Mathlib

Foundations

Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedDivisionRingMulActionWithZeroIsBoundedSMul