Theorems · Theorem · real analysis
ConvexOn.leftDeriv_le_rightDeriv_of_mem_interior
∀ {S : Set ℝ} {f : ℝ → ℝ} {x : ℝ},
ConvexOn ℝ S f → x ∈ interior S → derivWithin f (Set.Iio x) x ≤ derivWithin f (Set.Ioi x) x- Defined in
- Mathlib.Analysis.Convex.Deriv
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
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
- Set.ofPredproof · cited by 6,101
- Set.imageproof · cited by 5,609
- LT.lt.leproof · cited by 2,189
- Set.Ioistatement · cited by 1,463
- LT.lt.ne'proof · cited by 1,417
- Set.Iooproof · cited by 1,214
- Set.Iiostatement and proof · cited by 1,166
- InfSet.sInfproof · cited by 935
- LT.lt.neproof · cited by 872
- interiorstatement and proof · cited by 714
Cited by2
Results whose statement or proof uses this declaration.
- ConvexOn.isMinOn_of_rightDeriv_eq_zeroproof · cited by 1
- ConvexOn.isMinOn_of_leftDeriv_eq_zeroproof · cited by 0