Isomorphismes entre des espaces de mesures \`a valeurs vectorielles

Mohammad Daher

Isomorphismes entre des espaces de mesures \`a valeurs vectorielles

Functional Analysis 2025-08-26 v2

Authors: Mohammad Daher

Abstract

Let $(\Omega_1, \mathcal{F}_1, \mu_1)$ , $(\Omega_2, \mathcal{F}_2, \mu_2)$ be two probabilty spaces, $1\leq p\leq +\infty$ and $X$ a Banach space. In this work we show that $L^p(\mu_1, X)$ , $VB^p (\mu_1,X),$ $cabv(\mu_{1},X)$ are isomorphic to $L^p(\mu_2, X),$ $VB^p(\mu_2, X)$ , $cabc(\mu_2, X)$ respectively, if $L^1(\mu_1)$ is strongly isomorphic to $L^1(\mu_2)$ .

Keywords

vector-valued measures Banach space L^p space isomorphism probability space strong isomorphism VB^p space

Cite

@article{arxiv.1603.08979,
  title  = {Isomorphismes entre des espaces de mesures \`a valeurs vectorielles},
  author = {Mohammad Daher},
  journal= {arXiv preprint arXiv:1603.08979},
  year   = {2025}
}

Comments

There are some mistakes in the proofs

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