Lineability and spaceability on vector-measure spaces
Volume 219 / 2013
Studia Mathematica 219 (2013), 155-161
MSC: Primary 28A33; Secondary 46E27.
DOI: 10.4064/sm219-2-5
Abstract
It is proved that if $X$ is infinite-dimensional, then there exists an infinite-dimensional space of $X$-valued measures which have infinite variation on sets of positive Lebesgue measure. In term of spaceability, it is also shown that $ca(\mathcal {B}, \lambda , X) \setminus M_\sigma $, the measures with non-$\sigma $-finite variation, contains a closed subspace. Other considerations concern the space of vector measures whose range is neither closed nor convex. All of those results extend in some sense theorems of Muñoz Fernández et al. [Linear Algebra Appl. 428 (2008)].
