Non-Archimedean Probability

Milan Journal of Mathematics 81 (1):121-151 (2013)
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.
Keywords probability  infinitesimals  infinity  Kolmogorov  axioms  Regularity  non-standard models  fair lottery  non-Archimedean fields
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