Theorems · Theorem · functional analysis
Seminorm.convexOn
∀ {𝕜 : Type u_3} {E : Type u_7} [inst : NormedField 𝕜] [inst_1 : AddCommGroup E] [inst_2 : SMul ℝ 𝕜] [NormSMulClass ℝ 𝕜]
[inst_4 : Module 𝕜 E] [inst_5 : SMul ℝ E] [IsScalarTower ℝ 𝕜 E] (p : Seminorm 𝕜 E), ConvexOn ℝ Set.univ ⇑pA seminorm is convex. Also see convexOn_norm.
- Defined in
- Mathlib.Analysis.Seminorm
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Norm.normproof · cited by 5,413
- Set.univstatement and proof · cited by 3,945
- IsScalarTowerstatement and proof · cited by 3,896
- mul_oneproof · cited by 3,885
- NormedFieldstatement and proof · cited by 1,084
- Seminormstatement and proof · cited by 272
- norm_smulproof · cited by 242
- ConvexOnstatement · cited by 232
Cited by1
Results whose statement or proof uses this declaration.
- Seminorm.convex_ballproof · cited by 4