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(B; γX) n M, the measures with non-nite 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 Mu~noz Ferniandez et al. [Linear Algebra Appl. 428 (2008)].
Lineability and spaceability on vector-measure spaces
PUGLISI, DANIELE
2013-01-01
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(B; γX) n M, the measures with non-nite 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 Mu~noz Ferniandez et al. [Linear Algebra Appl. 428 (2008)].File in questo prodotto:
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