English

Non-Archimedean Probability

Probability 2021-07-30 v1

Abstract

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 zero- and unit-probability events pose no particular epistemological problems. 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.

Cite

@article{arxiv.1106.1524,
  title  = {Non-Archimedean Probability},
  author = {Vieri Benci and Leon Horsten and Sylvia Wenmackers},
  journal= {arXiv preprint arXiv:1106.1524},
  year   = {2021}
}

Comments

34 pages

R2 v1 2026-06-21T18:19:20.594Z