Vector Spaces of Non-measurable Functions
Source: Acta Mathematica Sinica, Volume 22, Number 6, November 2006 , pp. 1805-1808(4)
Abstract:We show that there exists an infinite dimensional vector space every non-zero element of which is a non-measurable function. Moreover, this vector space can be chosen to be closed and to have dimension β for any cardinality β. Some techniques involving measure theory and density characters of Banach spaces are used.
Document Type: Research article
Publication date: 2006-11-01