Extending $n$ times differentiable functions of several variables

summary:It is shown that $n$ times Peano differentiable functions defined on a closed subset of $\mathbb{R}^m$ and satisfying a certain condition on that set can be extended to $n$ times Peano differentiable functions defined on $\mathbb{R}^m$ if and only if the $n$th order Peano derivatives are Baire class one functions