Theorems · Theorem · functional analysis
convexOn_dist
∀ {E : Type u_1} [inst : SeminormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {s : Set E} (z : E),
Convex ℝ s → ConvexOn ℝ s fun z' => dist z' z- Defined in
- Mathlib.Analysis.Normed.Module.Convex
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 158 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.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedSpacestatement and proof · cited by 12,499
- Norm.normproof · cited by 5,413
- Set.preimageproof · cited by 4,946
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Dist.diststatement · cited by 1,539
- neg_negproof · cited by 960
- Convexstatement and proof · cited by 551
- ConvexOnstatement and proof · cited by 232
- add_sub_cancelproof · cited by 195
- dist_eq_normproof · cited by 182
Cited by2
Results whose statement or proof uses this declaration.
- convexOn_univ_distproof · cited by 2
- convexHull_exists_dist_geproof · cited by 1