Theorems · Theorem · measure theory

MeasureTheory.LocallyIntegrable.smul

∀ {X : Type u_1} {E : Type u_6} [inst : MeasurableSpace X] [inst_1 : TopologicalSpace X] [inst_2 : NormedAddCommGroup E]
  {μ : MeasureTheory.Measure X} {f : X → E} {𝕜 : Type u_9} [inst_3 : NormedAddCommGroup 𝕜] [inst_4 : SMulZeroClass 𝕜 E]
  [IsBoundedSMul 𝕜 E], MeasureTheory.LocallyIntegrable f μ → ∀ (c : 𝕜), MeasureTheory.LocallyIntegrable (c • f) μ

Defined in

Mathlib.MeasureTheory.Function.LocallyIntegrable

Cited by

1 results in Mathlib

Foundations

Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceTopologicalSpaceNormedAddCommGroupNormedAddCommGroupSMulZeroClassIsBoundedSMul