Theorems · Theorem · convex and discrete geometry
ConvexOn.continuousOn_Ico
∀ {f : ℝ → ℝ} {y z : ℝ}, ConvexOn ℝ (Set.Ico y z) f → ContinuousWithinAt f (Set.Ici y) y → ContinuousOn f (Set.Ico y z)- Defined in
- Mathlib.Analysis.Convex.Continuous
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- ContinuousOnstatement · cited by 1,411
- Set.Icistatement and proof · cited by 1,070
- Set.Icostatement and proof · cited by 799
- interiorproof · cited by 714
- ContinuousWithinAtstatement and proof · cited by 512
- ConvexOnstatement and proof · cited by 232
- ContinuousAt.continuousWithinAtproof · cited by 102
- eq_or_lt_of_leproof · cited by 92
- Ioo_mem_nhdsproof · cited by 27
- interior_Icoproof · cited by 12
- continuousWithinAt_iff_continuousAtproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- ConvexOn.continuousOn_Iccproof · cited by 1
- ConcaveOn.continuousOn_Icoproof · cited by 0