Real Algebraic and Analytic Geometry Preprint Server

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Submission: 2005, October 24.

Abstract:
Peano differentiability is a notion of higher order differentiability in the ordinary sense. H. W. Oliver gave sufficient conditions for the Peano derivative of order $m$ to be a derivative in the ordinary sense in the case of functions of a real variable. Here we generalize this theorem to functions of several variables.

Mathematics Subject Classification (2000): 26B05.

Keywords and Phrases: real Analysis, functions of several variables, Peano differentiability.

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