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A sigma-algebra which is related to the topology of a set. The Borel sigma-algebra is defined to be the sigma-algebra generated by the open sets (or equivalently, by the ...

If F is the Borel sigma-algebra on some topological space, then a measure m:F->R is said to be a Borel measure (or Borel probability measure). For a Borel measure, all ...

Sigma is the eighteenth letter of the ancient Greek alphabet. As an upper case letter (Sigma), it is used as a symbol for sums and series. As a lower case letter (sigma) it ...

Let X be a set. Then a sigma-algebra F is a nonempty collection of subsets of X such that the following hold: 1. X is in F. 2. If A is in F, then so is the complement of A. ...

A Borel set is an element of a Borel sigma-algebra. Roughly speaking, Borel sets are the sets that can be constructed from open or closed sets by repeatedly taking countable ...

A set equipped with a sigma-algebra of subsets.

The word "algebra" is a distortion of the Arabic title of a treatise by al-Khwārizmī about algebraic methods. In modern usage, algebra has several meanings. One use of the ...

A space which is isomorphic to a Borel subset B of a Polish space equipped with its sigma-algebra of Borel sets.

A Boolean sigma-algebra which possesses a measure.