Vol. 69, No. 3, pp. 207–213 (2017)

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On optimality of the index of sum, product, maximum, and minimum of finite Baire index functions

A. Zulijanto

Department of Mathematics, Universitas Gadjah Mada, Sekip Utara, Yogyakarta 55281, Indonesia E-mail: atokzulijanto@ugm.ac.id

Abstract: Chaatit, Mascioni, and Rosenthal defined finite Baire index for a bounded real-valued function f on a separable metric space, denoted by i(f), and proved that for any bounded functions f and g of finite Baire index, i(h)i(f)+i(g), where h is any of the functions f+g, fg, fg, fg. In this paper, we prove that the result is optimal in the following sense : for each n,k<ω, there exist functions f,g such that i(f)=n, i(g)=k, and i(h)=i(f)+i(g).

Keywords: Finite Baire index; oscillation index; Baire-1 functions.

Classification (MSC2000): 26A21; 54C30, 03E15

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Electronic fulltext finalized on: 20 Jun 2017. This page was last modified: 7 Jul 2017.

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