Isomorphismes entre des espaces de mesures à valeurs vectorielles

Abstract

Let $({\Omega }_1,{\mathcal{F}}_1,{\mu }_1)$, $({\Omega }_2,{\mathcal{F}}_2,{\mu }_2)$ be two probabilty spaces, $1\le p\le +\infty$ and $X$ a Banach space. In this work we show that $L^p({\mu }_1,X)$, $V{B}^p({\mu }_1,X),$ $cabv({\mu }_1,X)$ are isomorphic to $L^p({\mu }_2,X),$ $V{B}^p({\mu }_2,X)$, $cabc({\mu }_2,X)$ respectively, if $L^1({\mu }_1)$ is strongly isomorphic to $L^1({\mu }_2)$.

arXiv commentThere are some mistakes in the proofs