probability axioms

This parallels the fact that probabilities of mutually exclusive events are additive (see probability axioms).

See probability axioms.

The Bayesian calculus describes degrees of belief using the 'language' of probability; beliefs are positive, integrate to one, and obey probability axioms.

It can be shown that the set of prices is coherent when they satisfy the probability axioms and related results such as the inclusion-exclusion principle (but not necessarily countable additivity).

This price has to obey the probability axioms if you are not to face certain loss, as you would if you set a price above $1 (or a negative price).

The mathematics of probability can be developed on an entirely axiomatic basis that is independent of any interpretation: see the articles on probability theory and probability axioms for a detailed treatment.

In 1933, Kolmogorov published the book, 'Foundations of the Theory of Probability', laying the modern axiomatic probability axioms and establishing his reputation as the world's leading living expert in this field.

These concepts have been given an axiomatic mathematical derivation in probability theory (see probability axioms), which is used widely in such areas of study as mathematics, statistics, finance, gambling, science, artificial intelligence/machine learning and philosophy to, for example, draw inferences about the expected frequency of events.