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Vector measure Banach spaces containing a complemented copy of

Authors:	A Picó n C Piñ eiro

Institution:	Departamento de Matemáticas, Facultad de Ciencias Experimentales, Campus universitario de El Carmen, Universidad de Huelva, 21071, Huelva, Spain C. Piñeiro ; Departamento de Matemáticas, Facultad de Ciencias Experimentales, Campus universitario de El Carmen, Universidad de Huelva, 21071, Huelva, Spain

Abstract:	Let a Banach space and $\Sigma$ a $\sigma$ -algebra of subsets of a set $\Omega$ . We say that a vector measure Banach space $(\mathcal{M} (\Sigma , X ) , \Vert \cdot \Vert _\mathcal{M })$ has the bounded Vitaly-Hahn-Sacks Property if it satisfies the following condition: Every vector measure $m : \Sigma \longrightarrow X$ , for which there exists a bounded sequence $(m_{n})$ in $\mathcal{M } (\Sigma, X )$ verifying $\displaystyle\lim_{n \to \infty} m_{n} ( A ) = m(A)$ for all $A \in \Sigma$ , must belong to $\mathcal{M} (\Sigma, X)$ . Among other results, we prove that, if $\mathcal{M}(\Sigma, X)$ is a vector measure Banach space with the bounded V-H-S Property and containing a complemented copy of $c_{0}$ , then contains a copy of $c_{0}$ .

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