On the measurability of functions with quasi-continuous and upper semi-continuous vertical sections

Rok, strany: 2013, 793 - 798

Let $f:\mathbb{R}² \to \mathbb{R}$ be a function with upper semicontinuous and quasi-continuous vertical sections $f_x(t) = f(x,t)$, $t,x\in \mathbb{R}$. It is proved that if the horizontal sections $f^y(t) = f(t,y)$, $y,t\in \mathbb{R}$, are of Baire class $α$ (resp. Lebesgue measurable) [resp. with the Baire property] then $f$ is of Baire class $α + 2$ (resp. Lebesgue measurable and sup-measurable) [resp. has Baire property].

ISO 690:

Grande, Z. 2013. On the measurability of functions with quasi-continuous and upper semi-continuous vertical sections. In Mathematica Slovaca, vol. 63, no.4, pp. 793-798. 0139-9918. DOI: https://doi.org/10.2478/s12175-013-0135-0

APA:

Grande, Z. (2013). On the measurability of functions with quasi-continuous and upper semi-continuous vertical sections. Mathematica Slovaca, 63(4), 793-798. 0139-9918. DOI: https://doi.org/10.2478/s12175-013-0135-0