Semicontinuous integrands as jointly measurable maps

Carbonell-Nicolau, Oriol. "Semicontinuous integrands as jointly measurable maps." Commentationes Mathematicae Universitatis Carolinae 55.2 (2014): 189-193. <http://eudml.org/doc/261854>.

@article{Carbonell2014,
abstract = {Suppose that $(X,\mathcal \{A\})$ is a measurable space and $Y$ is a metrizable, Souslin space. Let $\mathcal \{A\}^u$ denote the universal completion of $\mathcal \{A\}$. For $x\in X$, let $\underline\{f\}(x,\cdot )$ be the lower semicontinuous hull of $f(x,\cdot )$. If $f:X\times Y\rightarrow \overline\{\mathbb \{R\}\}$ is $(\mathcal \{A\}^u\otimes \mathcal \{B\}(Y),\mathcal \{B\}(\overline\{\mathbb \{R\}\}))$-measurable, then $\underline\{f\}$ is $(\mathcal \{A\}^u\otimes \mathcal \{B\}(Y),\mathcal \{B\}(\overline\{\mathbb \{R\}\}))$-measurable.},
author = {Carbonell-Nicolau, Oriol},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {lower semicontinuous hull; jointly measurable function; measurable projection theorem; normal integrand; lower semicontinuous hull; jointly measurable function; measurable projection theorem; normal integrand},
language = {eng},
number = {2},
pages = {189-193},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Semicontinuous integrands as jointly measurable maps},
url = {http://eudml.org/doc/261854},
volume = {55},
year = {2014},
}

TY - JOUR
AU - Carbonell-Nicolau, Oriol
TI - Semicontinuous integrands as jointly measurable maps
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2014
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 55
IS - 2
SP - 189
EP - 193
AB - Suppose that $(X,\mathcal {A})$ is a measurable space and $Y$ is a metrizable, Souslin space. Let $\mathcal {A}^u$ denote the universal completion of $\mathcal {A}$. For $x\in X$, let $\underline{f}(x,\cdot )$ be the lower semicontinuous hull of $f(x,\cdot )$. If $f:X\times Y\rightarrow \overline{\mathbb {R}}$ is $(\mathcal {A}^u\otimes \mathcal {B}(Y),\mathcal {B}(\overline{\mathbb {R}}))$-measurable, then $\underline{f}$ is $(\mathcal {A}^u\otimes \mathcal {B}(Y),\mathcal {B}(\overline{\mathbb {R}}))$-measurable.
LA - eng
KW - lower semicontinuous hull; jointly measurable function; measurable projection theorem; normal integrand; lower semicontinuous hull; jointly measurable function; measurable projection theorem; normal integrand
UR - http://eudml.org/doc/261854
ER -