Czechoslovak Mathematical Journal, Vol. 53, No. 4, pp. 1009-1015, 2003

On Pettis integrability

J. C. Ferrando

Depto. Estadistica y Matematica Aplicada, Universidad Miguel Hernandez, E-03202 Elche (Alicante), Spain, e-mail:

Abstract: 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.

Keywords: Pettis integrable function space, copy of $c_0$, copy of $\ell_{\infty}$, countably additive vector measure, WRNP, CRP

Classification (MSC 2000): 46G10, 28B05

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