Continuity properties of Peano derivatives in several variables

Abstract

For a real-valued function of several real variables that is \(n\)-times Peano Differentiable, a sufficient condition is given for the Peano derivatives of order \(n\) to be Baire*1. An immediate consequence will be that the order \(n\) Peano derivatives of an \((n+1)\)-times Peano differentiable function are Baire*1.