Extending Peano derivatives: necessary and sufficient conditions

Tom 159 / 1999

Hans Volkmer Fundamenta Mathematicae 159 (1999), 219-229 DOI: 10.4064/fm-159-3-219-229


The paper treats functions which are defined on closed subsets of [0,1] and which are k times Peano differentiable. A necessary and sufficient condition is given for the existence of a k times Peano differentiable extension of such a function to [0,1]. Several applications of the result are presented. In particular, functions defined on symmetric perfect sets are studied.


  • Hans Volkmer

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