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 dimensionβ for any cardi...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 dimensionβ for any cardinalityβ. Some techniques involving measure theory and density characters of Banach spaces are used.展开更多
文摘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 dimensionβ for any cardinalityβ. Some techniques involving measure theory and density characters of Banach spaces are used.
