Representations of functions by derivatives

Agronsky, S. J.; Biskner, R.; Bruckner, A. M.; Mařík, J.

doi:10.1090/S0002-9947-1981-0594421-7

Representations of functions by derivatives
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by S. J. Agronsky, R. Biskner, A. M. Bruckner and J. Mařík PDF

Trans. Amer. Math. Soc. 263 (1981), 493-500 Request permission

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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