MathDB

Meticulous problem about lateral derivatives

Source: Bogdan Stan 2011, (modified)

October 7, 2019

functioncalculusderivativeintegrabilityConvexityside-continuity

Problem Statement

Let be an open interval

I

and a convex function

f:I\longrightarrow\mathbb{R} .

Prove that the lateral derivatives of

f

are left-continuous on

\mathbb{R}

and also right-continuous on

\mathbb{R} .

Marin Tolosi