Geodesic
Semicontinuous integrands as jointly measurable maps
Commentationes Mathematicae Universitatis Carolinae, Tome 55 (2014) no. 2, pp. 189-193 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 28A20, 54C30
Keywords: lower semicontinuous hull; jointly measurable function; measurable projection theorem; normal integrand 
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     author = {Carbonell-Nicolau, Oriol},
     title = {Semicontinuous integrands as jointly measurable maps},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {189--193},
     year = {2014},
     volume = {55},
     number = {2},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2014_55_2_a4/}
}
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Carbonell-Nicolau, Oriol. Semicontinuous integrands as jointly measurable maps. Commentationes Mathematicae Universitatis Carolinae, Tome 55 (2014) no. 2, pp. 189-193. http://geodesic.mathdoc.fr/item/CMUC_2014_55_2_a4/