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2010•Tatra Mountains Mathematical PublicationsOpen access

On some characterizations of Baire class one functions and Baire class one like functions

Anna Bąkowska, Ryszard Jerzy Pawlak

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Abstract

The basis of our considerations is a characterization of Baire class one functions presented by Pen-Yee Lee, Wee-Kee Tang, Doingsheng Zhao \cite{b1}. In the first part of this paper,  we will prove an analogous characterization for functions belonging to the class $B_1^{**}$. In the last part, we will consider various classes of functions connected with the characterization mentioned above, which permits to give a new characterization of Baire class one functions.

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What this paper is about

The basis of our considerations is a characterization of Baire class one functions presented by Pen-Yee Lee, Wee-Kee Tang, Doingsheng Zhao \cite{b1}. In the first part of this paper,  we will prove an analogous characterization for functions belonging to the class $B_1^{**}$. In the last part, we will consider various classes of functions connected with the characterization mentioned above, which permits to give a new characterization of Baire class one functions.

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Available abstract

The basis of our considerations is a characterization of Baire class one functions presented by Pen-Yee Lee, Wee-Kee Tang, Doingsheng Zhao \cite{b1}. In the first part of this paper,  we will prove an analogous characterization for functions belonging to the class $B_1^{**}$. In the last part, we will consider various classes of functions connected with the characterization mentioned above, which permits to give a new characterization of Baire class one functions.

Key concepts: Baire measure, Characterization (materials science), Mathematics, Baire category theorem, Baire space, Class (philosophy), Pure mathematics, Computer science

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