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Measures on effect algebras

In: Mathematica Slovaca, vol. 69, no. 1
Giuseppina Barbieri - Francisco Javier García-Pacheco - S. Moreno-Pulido

Details:

Year, pages: 2019, 159 - 170
Keywords:
effect algebra, lattice, poset, measure
About article:
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 $σ$-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.
How to cite:
ISO 690:
Barbieri, G., García-Pacheco, F., Moreno-Pulido, S. 2019. Measures on effect algebras. In Mathematica Slovaca, vol. 69, no.1, pp. 159-170. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0211

APA:
Barbieri, G., García-Pacheco, F., Moreno-Pulido, S. (2019). Measures on effect algebras. Mathematica Slovaca, 69(1), 159-170. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0211
About edition:
Published: 24. 1. 2019