Theorems · Theorem · convex and discrete geometry
ConcaveOn.locallyLipschitzOn_interior
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {C : Set E} {f : E → ℝ}
[FiniteDimensional ℝ E], ConcaveOn ℝ C f → LocallyLipschitzOn (interior C) f- Defined in
- Mathlib.Analysis.Convex.Continuous
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 175 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
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- FiniteDimensionalstatement and proof · cited by 1,854
- interiorstatement · cited by 714
- interior_subsetproof · cited by 171
- ConcaveOnstatement and proof · cited by 159
- isOpen_interiorproof · cited by 130
- LocallyLipschitzOnstatement · cited by 29
- Convex.interiorproof · cited by 14
- ConcaveOn.subsetproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- ConcaveOn.continuousOn_interiorproof · cited by 0
- ConcaveOn.locallyLipschitzproof · cited by 0