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Peano path derivatives

Author(s): Hajrudin Fejzic; Dan Rinne
Journal: Proc. Amer. Math. Soc. 125 (1997), 2651-2656.
MSC (1991): Primary 26A24; Secondary 26A21
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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:

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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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