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Non-Archimedean Probability

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2013

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Benci, Vieri
Wenmackers, Sylvia

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https://doi.org/10.1007/s00032-012-0191-x
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Milan Journal of Mathematics. Birkhäuser. 2013, 81(1), pp. 121-151. ISSN 1424-9286. eISSN 1424-9294. Available under: doi: 10.1007/s00032-012-0191-x

Zusammenfassung

We propose an alternative approach to probability theory closely related to the framework of numerosity theory: non-Archimedean probability (NAP). In our approach, unlike in classical probability theory, all subsets of an infinite sample space are measurable and only the empty set gets assigned probability zero (in other words: the probability functions are regular). We use a non-Archimedean field as the range of the probability function. As a result, the property of countable additivity in Kolmogorov’s axiomatization of probability is replaced by a different type of infinite additivity.

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100 Philosophie

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ISO 690BENCI, Vieri, Leon HORSTEN, Sylvia WENMACKERS, 2013. Non-Archimedean Probability. In: Milan Journal of Mathematics. Birkhäuser. 2013, 81(1), pp. 121-151. ISSN 1424-9286. eISSN 1424-9294. Available under: doi: 10.1007/s00032-012-0191-x
BibTex
@article{Benci2013-06NonAr-48885,
  year={2013},
  doi={10.1007/s00032-012-0191-x},
  title={Non-Archimedean Probability},
  number={1},
  volume={81},
  issn={1424-9286},
  journal={Milan Journal of Mathematics},
  pages={121--151},
  author={Benci, Vieri and Horsten, Leon and Wenmackers, Sylvia}
}
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