Lusin’s theorem for derivatives with respect to a continuous function
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- by V. Aversa and D. Preiss PDF
- Proc. Amer. Math. Soc. 127 (1999), 3229-3235 Request permission
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
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Additional Information
- V. Aversa
- Affiliation: Dipartimento di Matematica e Statistica, Via Cinzia, 80126 Napoli Italy
- Email: aversa@dmsna.dms.unina.it
- D. Preiss
- Affiliation: Department of Mathematics, University College London, Gower Street, London WCIE-6BT, England
- MR Author ID: 141890
- Email: dp@math.ucl.ac.uk
- 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. - Communicated by: Frederick W. Gehring
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 3229-3235
- MSC (1991): Primary 26A36; Secondary 26A24, 28E99
- DOI: https://doi.org/10.1090/S0002-9939-99-05086-8
- MathSciNet review: 1636926
Dedicated: Dedicated to Resia