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An approximate analog of a theorem of Khintchine

Chris Freiling; Dan Rinne — 1990

Fundamenta Mathematicae

Extending $n$ times differentiable functions of several variables

Hajrudin Fejzić; Dan Rinne; Clifford E. Weil — 1999

Czechoslovak Mathematical Journal

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

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An approximate analog of a theorem of Khintchine

Extending n times differentiable functions of several variables

Extending $n$ times differentiable functions of several variables