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1995/1996 Sums and products of quasi-continuous functions
Aleksander Maliszewski
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Real Anal. Exchange 21(1): 320-329 (1995/1996).


In this article two main results are proved. The first one is that each cliquish function \(f\colon \mathbb{R}^k \to \mathbb{R} \) is the sum of two quasi-continuous functions. It is also shown that we can moreover require that the summands preserve points of continuity of \(f\), are bounded provided that \(f\) is bounded and belong to the same class of Baire as \(f\) (if \(f\) is Borel measurable). The other main result is that each function \(f\colon \mathbb{R}^k \to \mathbb{R} \) which can be written as the product of finitely many quasi-continuous functions, can be expressed as the product of two quasi-continuous functions, and we can require that the factors belong to the same class of Baire as \(f\) (if \(f\) is Borel measurable).


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Aleksander Maliszewski. "Sums and products of quasi-continuous functions." Real Anal. Exchange 21 (1) 320 - 329, 1995/1996.


Published: 1995/1996
First available in Project Euclid: 3 July 2012

zbMATH: 0843.54019
MathSciNet: MR1377543

Primary: 26A21 , ‎28A15 , 54C08 , ‎54C30

Keywords: cliquish function , quasi-continuous function

Rights: Copyright © 1995 Michigan State University Press

Vol.21 • No. 1 • 1995/1996
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