Real Analysis Exchange

Sums and products of quasi-continuous functions

Aleksander Maliszewski

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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).

Article information

Real Anal. Exchange, Volume 21, Number 1 (1995), 320-329.

First available in Project Euclid: 3 July 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 54C08: Weak and generalized continuity 54C30: Real-valued functions [See also 26-XX] 28A15: Abstract differentiation theory, differentiation of set functions [See also 26A24] 26A21: Classification of real functions; Baire classification of sets and functions [See also 03E15, 28A05, 54C50, 54H05]

quasi-continuous function cliquish function


Maliszewski, Aleksander. Sums and products of quasi-continuous functions. Real Anal. Exchange 21 (1995), no. 1, 320--329.

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