# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Copies of $\ell _{\infty }$ in the space of Pettis integrable functions with integrals of finite variation

### Tom 210 / 2012

Studia Mathematica 210 (2012), 93-98 MSC: Primary 28B05; Secondary 46B03. DOI: 10.4064/sm210-1-6

#### Streszczenie

Let $( \varOmega ,\varSigma ,\mu )$ be a complete finite measure space and $X$ a Banach space. We show that the space of all weakly $\mu$-measurable (classes of scalarly equivalent) $X$-valued Pettis integrable functions with integrals of finite variation, equipped with the variation norm, contains a copy of $\ell _{\infty }$ if and only if $X$ does.

#### Autorzy

• Juan Carlos FerrandoCentro de Investigación Operativa