Theorems · Theorem · real analysis

LocallyBoundedVariationOn.fun_smul

∀ {α : Type u_2} [inst : LinearOrder α] {F : Type u_4} [inst_1 : NormedAddCommGroup F] [inst_2 : NormedSpace ℝ F]
  {𝕜 : Type u_6} {f : α → 𝕜} {g : α → F} [inst_3 : NormedRing 𝕜] [inst_4 : NormedAlgebra ℝ 𝕜] [inst_5 : Module 𝕜 F]
  [NormSMulClass 𝕜 F] [IsScalarTower ℝ 𝕜 F] {s : Set α},
  LocallyBoundedVariationOn f s → LocallyBoundedVariationOn g s → LocallyBoundedVariationOn (fun i => f i • g i) s

Eta-expanded form of LocallyBoundedVariationOn.smul

Defined in

Mathlib.Analysis.BoundedVariation

Cited by

0 results in Mathlib

Foundations

Depth 181 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderNormedAddCommGroupNormedSpaceNormedRingNormedAlgebraModuleNormSMulClassIsScalarTower