Abstract
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 language | English |
|---|---|
| Pages (from-to) | 121-136 |
| Number of pages | 16 |
| Journal | Quaestiones Mathematicae |
| Volume | 47 |
| Issue number | sup1 |
| DOIs | |
| Publication status | Published - 2024 |
Bibliographical note
Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-careOtherwise 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.
Keywords
- finitely additive
- modulus
- order bounded
- Vector measure