probability axioms are the foundations of probability theory introduced by Russian mathematician Andrey Kolmogorov in 1933. These axioms remain central...

This condition, called the T0 condition, is the weakest of the separation axioms. Nearly all topological spaces normally studied in mathematics are T0 spaces...

An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments...

following are named in Kolmogorov's honour: Fisher–Kolmogorov equation Johnson–Mehl–Avrami–Kolmogorov equation Kolmogorov axioms Kolmogorov equations (also known...

In mathematics, the axiom of choice, abbreviated AC or AoC, is an axiom of set theory equivalent to the statement that a Cartesian product of a collection...

axiom of choice included is abbreviated ZFC, where C stands for "choice", and ZF refers to the axioms of Zermelo–Fraenkel set theory with the axiom of...

where distinct points have disjoint neighbourhoods. Of the many separation axioms that can be imposed on a topological space, the "Hausdorff condition" (T2)...

separation axioms. These are sometimes called Tychonoff separation axioms, after Andrey Tychonoff. The separation axioms are not fundamental axioms like those...

consistent with the original probability measure and satisfies all the Kolmogorov axioms. This conditional probability measure also could have resulted by...

to Kolmogorov complexity based on Blum axioms (Blum 1967) was introduced by Mark Burgin in the paper presented for publication by Andrey Kolmogorov. We...

is known as Axiom T3. The term "T3 space" usually means "a regular Hausdorff space". These conditions are examples of separation axioms. A topological...

theory. The solution illustrates some basic principles, including the Kolmogorov axioms. The problem can be reframed by describing the boxes as each having...

twentieth century, of which Zermelo–Fraenkel set theory (with or without the axiom of choice) is still the best-known and most studied. Set theory is commonly...

distinguishable points. The properties T1 and R0 are examples of separation axioms. Let X be a topological space and let x and y be points in X. We say that...

of mathematics, a normal space is a topological space X that satisfies Axiom T4: every two disjoint closed sets of X have disjoint open neighborhoods...

The axiom of constructibility is a possible axiom for set theory in mathematics that asserts that every set is constructible. The axiom is usually written...

similar to a probability distribution but which relaxes some of Kolmogorov's axioms of probability theory. Quasiprobabilities share several of general...

Tarski's axioms are an axiom system for Euclidean geometry, specifically for that portion of Euclidean geometry that is formulable in first-order logic...

In mathematical logic, an axiom schema (plural: axiom schemata or axiom schemas) generalizes the notion of axiom. An axiom schema is a formula in the metalanguage...

(that is, of Zermelo–Fraenkel set theory with the axiom of choice excluded), and also that the axiom of choice and the generalized continuum hypothesis...

mathematics and logic, an axiomatic system is any set of primitive notions and axioms to logically derive theorems. A theory is a consistent, relatively-self-contained...

finitely many axioms, the axiom schema of class comprehension is first replaced with finitely many class existence axioms. Then these axioms are used to...

Hilbert's axioms are a set of 20 assumptions proposed by David Hilbert in 1899 in his book Grundlagen der Geometrie (tr. The Foundations of Geometry) as...

theory, Martin's axiom, introduced by Donald A. Martin and Robert M. Solovay, is a statement that is independent of the usual axioms of ZFC set theory...

axiom schema containing a separate axiom for each possible predicate. The article Peano axioms contains further discussion of this issue. The axiom of...

The history of the separation axioms in general topology has been convoluted, with many meanings competing for the same terms and many terms competing...

schools (see Motivations and epistemic status below). A large cardinal axiom is an axiom stating that there exists a cardinal (or perhaps many of them) with...

mathematics, specifically in class theories, the axiom of global choice is a stronger variant of the axiom of choice that applies to proper classes of sets...

1093/comjnl/bxh124, ISSN 0010-4620 Martin-Löf, Per (2005), "100 years of Zermelo's axiom of choice: what was the problem with it?", The Computer Journal, 49 (3):...

by the axiom of equality. Now (induction hypothesis), if 0 were equal to a certain natural number n, then 1 would be equal to n + 1, (Peano axiom: Sm = Sn...