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Keywords:
Pettis integrable function space; copy of $c_0$; copy of $\ell _{\infty }$; countably additive vector measure; WRNP; CRP
Pettis integrable function space; copy of $c_0$; copy of $\ell _{\infty }$; countably additive vector measure; WRNP; CRP
Summary:
Assuming that $(\Omega , \Sigma , \mu )$ is a complete probability space and $X$ a Banach space, in this paper we investigate the problem of the $X$-inheritance of certain copies of $c_0$ or $\ell _{\infty }$ in the linear space of all [classes of] $X$-valued $\mu $-weakly measurable Pettis integrable functions equipped with the usual semivariation norm.
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