Abstract
In this paper, the classical theory, due to R. de POSSEL [11][12], of abstract derivation basis with VITALI properties, is systematically generalized with a functional formulation. That is to say that the derivation by means of suitable families of measurable sets is replaced by a derivation using measurable functions. A theorem which gives various caracterizations of that functional basis of weak VITALI type includes a theorem obtained by R. de POSSEL [13] about this kind of derivation. This result leads to the introduction of VITALI conditions of functional type in a derivation theorem of N. DUNFORD and J. T. SCHWARTZ [3].
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Gapaillard, J. Derivation fonctionnelle abstraite. Manuscripta Math 12, 351–386 (1974). https://doi.org/10.1007/BF01171081
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DOI: https://doi.org/10.1007/BF01171081