## Real Analysis Exchange

### Sums and products of quasi-continuous functions

Aleksander Maliszewski

#### Abstract

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

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

Dates
First available in Project Euclid: 3 July 2012