Convex_Real_Function_is_Continuous

import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.Convex.Function

import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.Convex.Function

theorem Convex_Real_Function_is_Continuous (f : ℝ → ℝ) (a b : ℝ) (hab : a < b) (hf : ConvexOn ℝ (Set.Ioo a b) f) : ContinuousOn f (Set.Ioo a b) := by sorry