Theorems · Theorem · real analysis
ConvexOn.differentiableWithinAt_Ioi_of_mem_interior
∀ {S : Set ℝ} {f : ℝ → ℝ} {x : ℝ}, ConvexOn ℝ S f → x ∈ interior S → DifferentiableWithinAt ℝ f (Set.Ioi x) x- Defined in
- Mathlib.Analysis.Convex.Deriv
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.Ioistatement · cited by 1,463
- interiorstatement and proof · cited by 714
- DifferentiableWithinAtstatement · cited by 453
- ConvexOnstatement and proof · cited by 232
- HasDerivWithinAt.differentiableWithinAtproof · cited by 19
- ConvexOn.hasDerivWithinAt_sInf_slope_of_mem_interiorproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- ConvexOn.rightDeriv_le_slope_of_mem_interiorproof · cited by 1
- ConvexOn.hasDerivWithinAt_rightDeriv_of_mem_interiorproof · cited by 0