# 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 2^{X}) on that set.

**AKA:**Field of Sets.**See:**Formal Set System, Set Measure Space, Probability Space.

## References

- (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Field_of_sets
- 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.

- In mathematics a field of sets is a pair <