Parametrization of Riemann-measurable
selections for multifunctions of two variables
with application to differential inclusions
Annales Polonici Mathematici, Tome 83 (2004) no. 2, pp. 179-187
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We consider a multifunction $F:T\times X\to 2^E$, where $T$, $X$ and $E$ are separable metric spaces, with $E$ complete. Assuming that $F$ is jointly measurable in the product and a.e. lower semicontinuous in the second variable, we establish the existence of a selection for $F$ which is measurable with respect to the first variable and a.e. continuous with respect to the second one. Our result is in the spirit of [11], where multifunctions of only one variable are considered.
Keywords:
consider multifunction times where separable metric spaces complete assuming jointly measurable product lower semicontinuous second variable establish existence selection which measurable respect first variable continuous respect second result spirit where multifunctions only variable considered
Affiliations des auteurs :
Giovanni Anello 1 ; Paolo Cubiotti 1
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author = {Giovanni Anello and Paolo Cubiotti},
title = {Parametrization of {Riemann-measurable
} selections for multifunctions of two variables
with application to differential inclusions},
journal = {Annales Polonici Mathematici},
pages = {179--187},
publisher = {mathdoc},
volume = {83},
number = {2},
year = {2004},
doi = {10.4064/ap83-2-8},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ap83-2-8/}
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Giovanni Anello; Paolo Cubiotti. Parametrization of Riemann-measurable selections for multifunctions of two variables with application to differential inclusions. Annales Polonici Mathematici, Tome 83 (2004) no. 2, pp. 179-187. doi: 10.4064/ap83-2-8
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