Measures on effect algebras
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914672507092992 |
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| author | Barbieri, Giuseppina García-Pacheco, Francisco Javier Moreno-Pulido, Soledad |
| author_facet | Barbieri, Giuseppina García-Pacheco, Francisco Javier Moreno-Pulido, Soledad |
| contents | We study measures defined on effect algebras. We characterize real-valued measures on effect algebras and find a class of effect algebras, that include the natural effect algebras of sets, on which sigma-additive measures with values in a finite dimensional Banach space are always bounded. We also prove that in effect algebras the Nikodym and the Grothendieck properties together imply the Vitali-Hahn-Saks property, and find an example of an effect algebra verifying the Vitali-Hahn-Saks property but failing to have the Nikodym property. Finally, we define the concept of variation for vector measures on effect algebras proving that in effect algebras verifying the Riesz Decomposition Property, the variation of a finitely additive vector measure is a finitely additive positive measure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_06391 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Measures on effect algebras Barbieri, Giuseppina García-Pacheco, Francisco Javier Moreno-Pulido, Soledad Functional Analysis We study measures defined on effect algebras. We characterize real-valued measures on effect algebras and find a class of effect algebras, that include the natural effect algebras of sets, on which sigma-additive measures with values in a finite dimensional Banach space are always bounded. We also prove that in effect algebras the Nikodym and the Grothendieck properties together imply the Vitali-Hahn-Saks property, and find an example of an effect algebra verifying the Vitali-Hahn-Saks property but failing to have the Nikodym property. Finally, we define the concept of variation for vector measures on effect algebras proving that in effect algebras verifying the Riesz Decomposition Property, the variation of a finitely additive vector measure is a finitely additive positive measure. |
| title | Measures on effect algebras |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2402.06391 |