Valov proved a general version of Arvanitakis's simultaneous selection theorem which is a common generalization of both Michael's selection theorem and Dugundji's extension theorem. We show that Valov's theorem can be extended by applying an argument by means of Pettis integrals due to Repovš, Semenov and Shchepin.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm215-1-1,
author = {Takamitsu Yamauchi},
title = {On a simultaneous selection theorem},
journal = {Studia Mathematica},
volume = {215},
year = {2013},
pages = {1-9},
zbl = {1270.54026},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm215-1-1}
}
Takamitsu Yamauchi. On a simultaneous selection theorem. Studia Mathematica, Tome 215 (2013) pp. 1-9. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm215-1-1/