We consider a multifunction , 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap83-2-8,
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},
volume = {83},
year = {2004},
pages = {179-187},
zbl = {1114.28009},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap83-2-8}
}
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) pp. 179-187. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap83-2-8/