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Peano path derivatives


Authors: Hajrudin Fejzic and Dan Rinne
Journal: Proc. Amer. Math. Soc. 125 (1997), 2651-2656
MSC (1991): Primary 26A24; Secondary 26A21
DOI: https://doi.org/10.1090/S0002-9939-97-03878-1
MathSciNet review: 1396976
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Abstract: In this paper we introduce Peano path derivatives as a natural extension of the notion of path derivatives. We give a sufficient condition on a system of paths to ensure the corresponding Peano path derivative is Baire 1. As consequences, we obtain that unilateral approximate and unilateral $I$-approximate Peano derivatives are Baire one.


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

  • 1. A. M. Bruckner, R. J. O'Malley and B. S. Thomson, Path Derivatives: A Unified View of Certain Generalized Derivatives, Trans. Amer Math. Soc. Vol. 283 1 (1984), 97-125. MR 86d:26007
  • 2. H. Fejzi\'{c}, The Peano Derivatives, Ph.D. Dissertation, Michigan State University (1992).
  • 3. E. Lazarow, On the Baire Class of ${\cal I}$ -approximate Derivatives, Proc. Amer. Math. Soc. Vol. 100 4 (1987), 669-674. MR 88h:26001
  • 4. W. Poreda, E. Wagner-Bojakowska, and W. Wilczy\'{n}ski, A Category Analogue of the Density Topology, Fund. Math. Vol. 128 (1985), 167-173. MR 87b:54034

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Additional Information

Hajrudin Fejzic
Affiliation: Department of Mathematics, California State University, San Bernardino, California 92407
Email: hfejzic@wiley.csusb.edu

Dan Rinne
Affiliation: Department of Mathematics, California State University, San Bernardino, California 92407
Email: drinne@wiley.csusb.edu

DOI: https://doi.org/10.1090/S0002-9939-97-03878-1
Received by editor(s): October 25, 1995
Received by editor(s) in revised form: March 20, 1996
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1997 American Mathematical Society

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