Theorems · Theorem · real analysis
LocallyBoundedVariationOn.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 (f • g) s- Defined in
- Mathlib.Analysis.BoundedVariation
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Modulestatement and proof · cited by 20,661
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- LinearOrderstatement and proof · cited by 8,572
- IsScalarTowerstatement and proof · cited by 3,896
- NormedAlgebrastatement and proof · cited by 1,165
- NormedRingstatement and proof · cited by 924
- NormSMulClassstatement and proof · cited by 107
- ContinuousLinearMap.lsmulproof · cited by 66
- LocallyBoundedVariationOnstatement and proof · cited by 41
Cited by1
Results whose statement or proof uses this declaration.
- LocallyBoundedVariationOn.fun_smulproof · cited by 0