JournalszaaVol. 33, No. 2pp. 171–176

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

  • Zbigniew Grande

    Kazimierz Wielki University, Bydgoszcz, Poland
Pointwise Limits of Sequences of Right-Continuous Functions and Measurability of Functions of Two Variables cover
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Abstract

In this article I prove that the pointwise limit f ⁣:RRf\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 ⁣:R2Rg\colon\mathbb R^2 \to \mathbb R whose vertical sections gxg_x, xRx\in \mathbb R, are derivatives and horizontal sections gyg^y, yRy\in \mathbb R, are pointwise limits of sequences of right-continuous functions, are measurable and sup-measurable in the sense of Lebesgue.

Cite this article

Zbigniew Grande, Pointwise Limits of Sequences of Right-Continuous Functions and Measurability of Functions of Two Variables. Z. Anal. Anwend. 33 (2014), no. 2, pp. 171–176

DOI 10.4171/ZAA/1505