Nonmeasurability in Banach spaces

Abstract

We show that for a $\sigma$-ideal $\ci$ with a Steinhaus property defined on Banach space, if two non-homeomorphic Banach with the same cardinality of the Hamel basis then there is a $\ci$ nonmeasurable subset as image by any isomorphism between of them. Our results generalize results from [2]

arXiv comment6 pages