The modulus of a vector measure

Ben de Pagter*, Werner J. Ricker

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review


It is known that if L is a Dedekind complete Riesz space and (Ω, Σ) is a measurable space, then the partially ordered linear space of all L-valued, finitely additive and order bounded vector measures m on Σ is also a Dedekind complete Riesz space (for the natural operations). In particular, the modulus |m|o of m exists in this space of measures and |m|o is given by a well known formula. Some 20 years ago L. Drewnowski and W. Wnuk asked the question (for L not Dedekind complete) if there is an m for which |m|o exists but, |m|o is not given by the usual formula? We show that such a measure m does indeed exist.

Original languageEnglish
Pages (from-to)121-136
Number of pages16
JournalQuaestiones Mathematicae
Issue numbersup1
Publication statusPublished - 2024

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


  • finitely additive
  • modulus
  • order bounded
  • Vector measure


Dive into the research topics of 'The modulus of a vector measure'. Together they form a unique fingerprint.

Cite this