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

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

#### 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.

First Page:
Primary Subjects: 26B05, 26A15
Full-text: Open access

Permanent link to this document: http://projecteuclid.org/euclid.rae/1230995399
Mathematical Reviews number (MathSciNet): MR1778517

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Project Euclid: euclid.pjm/1102867878