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Non-Archimedean Probability |
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| Authors: | Vieri Benci Leon Horsten Sylvia Wenmackers |
| Institution: | 1. Dipartimento di Matematica Applicata, Universitá degli Studi di Pisa, Via F. Buonarroti 1/c, 56127, Pisa, Italy 2. Department of Mathematics, College of Science, King Saud University, 11451, Riyadh, Saudi Arabia 3. Department of Philosophy, University of Bristol, 43 Woodland Rd, BS81UU, Bristol, United Kingdom 4. Faculty of Philosophy, University of Groningen, Oude Boteringestraat 52, 9712 GL, Groningen, The Netherlands |
| 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 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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