Integration in Hilbert generated Banach spaces

Robert Deville, José Rodri guez

Research output: Contribution to journalArticlepeer-review


We prove that McShane and Pettis integrability are equivalent for functions taking values in a subspace of a Hilbert generated Banach space. This generalizes simultaneously all previous results on such equivalence. On the other hand, for any super-reflexive generated Banach space having density character greater than or equal to the continuum, we show that Birkhoff integrability lies strictly between Bochner and McShane integrability. Finally, we give a ZFC example of a scalarly null Banach space-valued function (defined on a Radon probability space) which is not McShane integrable.

Original languageEnglish (US)
Pages (from-to)285-306
Number of pages22
JournalIsrael Journal of Mathematics
Issue number1
StatePublished - 2010

ASJC Scopus subject areas

  • General Mathematics


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