  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.
