Probability Axioms
In probability theory, the probability P of some event E, denoted, is usually defined in such a way that P satisfies the Kolmogorov axioms, named after the famous Russian mathematician Andrey Kolmogorov, which are described below.
These assumptions can be summarised as: Let (Ω, F, P) be a measure space with P(Ω)=1. Then (Ω, F, P) is a probability space, with sample space Ω, event space F and probability measure P.
An alternative approach to formalising probability, favoured by some Bayesians, is given by Cox's theorem.
Read more about Probability Axioms: First Axiom, Second Axiom, Third Axiom, Proofs, More Consequences
Famous quotes containing the words probability and/or axioms:
“Liberty is a blessing so inestimable, that, wherever there appears any probability of recovering it, a nation may willingly run many hazards, and ought not even to repine at the greatest effusion of blood or dissipation of treasure.”
—David Hume (1711–1776)
““I tell you the solemn truth that the doctrine of the Trinity is not so difficult to accept for a working proposition as any one of the axioms of physics.””
—Henry Brooks Adams (1838–1918)