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In the paper a theorem of Piccard's type is proved and, consequently, thecontinuity of $\mathcal{D}$-measurable polynomial functions of $n$-th order aswell as $\mathcal{D}$-measurable $n$-convex functions is shown. The paperrefers to the papers \cite{Gajda} and \cite{EJ}.

A theorem of Piccard's type and its applications to polynomial functions and convex functions of higher orders