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Proceedings of the American Mathematical Society

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Lusin's theorem for derivatives
with respect to a continuous function

Authors: V. Aversa and D. Preiss
Journal: Proc. Amer. Math. Soc. 127 (1999), 3229-3235
MSC (1991): Primary 26A36; Secondary 26A24, 28E99
Published electronically: May 4, 1999
MathSciNet review: 1636926
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Abstract | References | Similar Articles | Additional Information

Abstract: For a nowhere constant continuous function $g$ on a real interval $I$ and for a Borel measure $\mu$ on $I$, we give simple necessary and sufficient conditions guaranteeing, for any Borel function $f$ on $I$, the existence of a continuous function $F$ on $I$ such that the derivative of $F$ with respect to $g$ is, $\mu$ almost everywhere, equal to $f$.

References [Enhancements On Off] (What's this?)

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  • 2. V. Aversa, Sugli insiemi di peso nullo rispetto ad una funzione continua Ric. Mat. 26, 79-84, 1977. MR 58:1070
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Additional Information

V. Aversa
Affiliation: Dipartimento di Matematica e Statistica, Via Cinzia, 80126 Napoli Italy

D. Preiss
Affiliation: Department of Mathematics, University College London, Gower Street, London WCIE-6BT, England

Keywords: Relative derivatives
Received by editor(s): January 22, 1998
Published electronically: May 4, 1999
Additional Notes: The first author was supported by M.P.I fund.
The second author was a visiting Professor at Dipartimento di Matematica e Applicazioni dell’Università di Napoli.
Dedicated: Dedicated to Resia
Communicated by: Frederick W. Gehring
Article copyright: © Copyright 1999 American Mathematical Society

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