Theorems · Theorem · convex and discrete geometry
ConvexOn.continuousOn_Ioc
∀ {f : ℝ → ℝ} {y z : ℝ}, ConvexOn ℝ (Set.Ioc y z) f → ContinuousWithinAt f (Set.Iic z) z → ContinuousOn f (Set.Ioc 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.Iicstatement and proof · cited by 1,111
- Set.Iocstatement and proof · cited by 971
- 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_Iocproof · cited by 10
- continuousWithinAt_iff_continuousAtproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- ConvexOn.continuousOn_Iccproof · cited by 1
- ConcaveOn.continuousOn_Iocproof · cited by 0