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Zeitschrift für Analysis und ihre Anwendungen


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Volume 33, Issue 2, 2014, pp. 171–176
DOI: 10.4171/ZAA/1505

Published online: 2014-04-25

Pointwise Limits of Sequences of Right-Continuous Functions and Measurability of Functions of Two Variables

Zbigniew Grande[1]

(1) Kazimierz Wielki University, Bydgoszcz, Poland

In this article I prove that the pointwise limit $f\colon\mathbb R \to \mathbb R$ of a sequence of right-continuous functions has some special property (G) and that bounded functions of two variables $g\colon\mathbb R^2 \to \mathbb R$ whose vertical sections $g_x$, $x\in \mathbb R$, are derivatives and horizontal sections $g^y$, $y\in \mathbb R$, are pointwise limits of sequences of right-continuous functions, are measurable and sup-measurable in the sense of Lebesgue.

Keywords: Pointwise convergence, right-continuity, Baire 1 class, derivative, approximate continuity, measurability of functions of two variables

Grande Zbigniew: Pointwise Limits of Sequences of Right-Continuous Functions and Measurability of Functions of Two Variables. Z. Anal. Anwend. 33 (2014), 171-176. doi: 10.4171/ZAA/1505