Theorems · Theorem · convex and discrete geometry
ConcaveOn.locallyLipschitzOn_iff_continuousOn
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {C : Set E} {f : E → ℝ},
IsOpen C → ConcaveOn ℝ C f → (LocallyLipschitzOn C f ↔ ContinuousOn f C)- Defined in
- Mathlib.Analysis.Convex.Continuous
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- 0 results in Mathlib
- Foundations
- Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- IsOpenstatement and proof · cited by 2,400
- ContinuousOnstatement · cited by 1,411
- ConcaveOnstatement and proof · cited by 159
- LocallyLipschitzOnstatement · cited by 29
- ConcaveOn.negproof · cited by 29
- ConvexOn.locallyLipschitzOn_iff_continuousOnproof · cited by 1
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