Non-Archimedean Probability

Details Non-Archimedean Probability Non-Archimedean Probability

2011-06-08

arxiv.org/abs/1106.1524v1

Mathematics

Probability

34 pages

Scientific paper

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.

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