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Borel Set


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 unions and intersections. Formally, the class B of Borel sets in Euclidean R^n is the smallest collection of sets that includes the open and closed sets such that if E, E_1, E_2, ... are in B, then so are  union _(i=1)^inftyE_i,  intersection _(i=1)^inftyE_i, and R^n\E, where F\E is a set difference (Croft et al. 1991).

The set of rational numbers is a Borel set, as is the Cantor set.


See also

Closed Set, Open Set, Standard Space

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References

Croft, H. T.; Falconer, K. J.; and Guy, R. K. Unsolved Problems in Geometry. New York: Springer-Verlag, p. 3, 1991.

Referenced on Wolfram|Alpha

Borel Set

Cite this as:

Weisstein, Eric W. "Borel Set." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BorelSet.html

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