Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Representations of functions by derivatives

Authors: S. J. Agronsky, R. Biskner, A. M. Bruckner and J. Mařík
Journal: Trans. Amer. Math. Soc. 263 (1981), 493-500
MSC: Primary 26A24; Secondary 26A21, 26A27
MathSciNet review: 594421
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Abstract: Let $ \Delta '$ be the class of all derivatives. The main goal of this paper is the investigation of the vector space generated by $ \Delta '$ and O'Malley's class $ B_1^ \ast $; this space is identical with our system $ [\Delta ']$. We show, in particular, that each approximately continuous function and each approximate derivative belongs to $ [\Delta ']$ and that $ [\Delta ']$ is the system of all functions of the form $ g' + hk'$, where $ g$, $ h$ and $ k$ are differentiable.

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Keywords: Derivatives, approximate derivatives, approximately continuous functions, functions of Baire class $ 1$
Article copyright: © Copyright 1981 American Mathematical Society