Abstract
It is proved that for a functionf defined inR k, and for every derivation baseD, there exists an additive interval function wich is a primitive off onD. This generalizes a result of Sierpinski.
References
Sierpiński W.,Sur une propriété des fontions quelconques d’une variable réelle, Fund. Mat. XXV, (1935), 1–4.
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Gruppo di ricerca diretto dal Prof. V. Aversa con fondo MPI.
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Tartaglia, M. Una fuzione qualunque come densità di una funzione di intervallo. Rend. Circ. Mat. Palermo 40, 465–469 (1991). https://doi.org/10.1007/BF02845081
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DOI: https://doi.org/10.1007/BF02845081