For multifunctions $F:\/T\times X\to 2^Y$, measurable in the first variable and semicontinuous in the second one, a relation is established between being product measurable and being superpositionally measurable.
@article{118473, author = {Wojciech Zygmunt}, title = {On superpositionally measurable semi-Carath\'eodory multifunctions}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {33}, year = {1992}, pages = {73-77}, zbl = {0756.28008}, mrnumber = {1173749}, language = {en}, url = {http://dml.mathdoc.fr/item/118473} }
Zygmunt, Wojciech. On superpositionally measurable semi-Carathéodory multifunctions. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) pp. 73-77. http://gdmltest.u-ga.fr/item/118473/
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