Theorems · Theorem · convex and discrete geometry
ConvexOn.locallyLipschitzOn_iff_continuousOn
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {C : Set E} {f : E → ℝ},
IsOpen C → ConvexOn ℝ C f → (LocallyLipschitzOn C f ↔ ContinuousOn f C)- Defined in
- Mathlib.Analysis.Convex.Continuous
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- nhdsproof · cited by 5,554
- Set.Nonemptyproof · cited by 2,627
- IsOpenstatement and proof · cited by 2,400
- absproof · cited by 1,814
- ContinuousOnstatement and proof · cited by 1,411
- ContinuousAtproof · cited by 697
- Set.eq_empty_or_nonemptyproof · cited by 248
- Filter.IsBoundedUnderproof · cited by 247
Cited by1
Results whose statement or proof uses this declaration.
- ConcaveOn.locallyLipschitzOn_iff_continuousOnproof · cited by 0