Czechoslovak Mathematical Journal, Vol. 49, No. 4, pp. 825-830, 1999

Extending $n$ times differentiable functions of several variables

Hajrudin Fejzic, Dan Rinne, Clifford Weil

Department of Mathematics, Michigan State University, East Lansing, Michigan 48824-1027, U.S.A

Abstract: 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.

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