Non-Archimedean Probability

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• 作者：Vieri Benci (1) (2)
  Leon Horsten (3)
  Sylvia Wenmackers (4)
  
• 关键词：60A05 ; 03H05 ; Probability ; axioms of Kolmogorov ; nonstandard models ; fair lottery ; non ; Archimedean fields
• 刊名：Milan Journal of Mathematics
• 出版年：2013
• 出版时间：June 2013
• 年：2013
• 卷：81
• 期：1
• 页码：121-151
• 全文大小：380KB
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• 作者单位：Vieri Benci (1) (2)
  Leon Horsten (3)
  Sylvia Wenmackers (4)
  
  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
  
• ISSN：1424-9294

文摘

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.