Theorems · Theorem · measure theory

MeasureTheory.Integrable.smul

∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : NormedAddCommGroup β]
  {𝕜 : Type u_8} [inst_1 : NormedAddCommGroup 𝕜] [inst_2 : SMulZeroClass 𝕜 β] [IsBoundedSMul 𝕜 β] (c : 𝕜) {f : α → β},
  MeasureTheory.Integrable f μ → MeasureTheory.Integrable (c • f) μ

Defined in

Mathlib.MeasureTheory.Function.L1Space.Integrable

Cited by

21 results in Mathlib

Foundations

Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedAddCommGroupSMulZeroClassIsBoundedSMul