Set Field

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A Set Field is a 2-Tuple composed of a set (X) and a Sigma Field (a Subset of 2X) on that set.


  • (Wikipedia, 2009) ⇒
    • In mathematics a field of sets is a pair <X, Ƒ> where [math]\displaystyle{ X }[/math] is a set and Ƒ is an algebra over [math]\displaystyle{ X }[/math] i.e., a non-empty subset of the power set of [math]\displaystyle{ X }[/math] closed under the intersection and union of pairs of sets and under complements of individual sets. In other words Ƒ forms a subalgebra of the power set Boolean algebra of X. (Many authors refer to Ƒ itself as a field of sets.) Elements of [math]\displaystyle{ X }[/math] are called points and those of Ƒ are called complexes.
    • Fields of sets play an essential role in the representation theory of Boolean algebras. Every Boolean algebra can be represented as a field of sets.