## Real Analysis Exchange

### On the Measurability of Functions f:ℝ²→ℝ Having Pawlak’s Property in One Variable

Zbigniew Grande

#### Abstract

In this article we present a condition on the sections $f^y$ of a function $f: \mathbb{R}^2 \to \mathbb{R}$ having Lebesgue measurable sections $f_x$ and quasicontinuous sections $f^y$ which implies the measurability of $f$. This condition is more general than the Baire$^{**}_1$ property introduced by R. Pawlak in [7]. Some examples of quasicontinuous functions satisfying this condition and discontinuous on the sets of positive measure are given.

#### Article information

Source
Real Anal. Exchange, Volume 25, Number 2 (1999), 647-652.

Dates
First available in Project Euclid: 3 January 2009

Permanent link to this document
https://projecteuclid.org/euclid.rae/1230995399

Mathematical Reviews number (MathSciNet)
MR1778517

#### Citation

Grande, Zbigniew. On the Measurability of Functions f :ℝ²→ℝ Having Pawlak’s Property in One Variable. Real Anal. Exchange 25 (1999), no. 2, 647--652. https://projecteuclid.org/euclid.rae/1230995399

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