Theorems · Theorem · convex and discrete geometry
ConvexOn.locallyLipschitzOn
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {C : Set E} {f : E → ℝ}
[FiniteDimensional ℝ E], IsOpen C → ConvexOn ℝ C f → LocallyLipschitzOn C f- Defined in
- Mathlib.Analysis.Convex.Continuous
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites36
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- nhdsproof · cited by 5,554
- Set.rangeproof · cited by 4,705
- LE.le.transproof · cited by 3,151
- Set.Nonemptyproof · cited by 2,627
- IsOpenstatement and proof · cited by 2,400
- FiniteDimensionalstatement and proof · cited by 1,854
- absproof · cited by 1,814
Cited by3
Results whose statement or proof uses this declaration.
- ConcaveOn.locallyLipschitzOnproof · cited by 2
- ConvexOn.locallyLipschitzOn_interiorproof · cited by 2
- ConvexOn.continuousOnproof · cited by 1