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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 ...

An outer measure mu on R^n is Borel regular if, for each set X subset R^n, there exists a Borel set B superset X such that mu(B)=mu(X). The d-dimensional Hausdorff outer ...

If a field has the property that, if the sets A_1, ..., A_n, ... belong to it, then so do the sets A_1+...+A_n+... and A_1...A_n..., then the field is called a Borel field ...

A theorem which specifies the structure of the generic unitary representation of the Weyl relations and thus establishes the equivalence of Heisenberg's matrix mechanics and ...

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 ...

The term Borel hierarchy is used to describe a collection of subsets of R defined inductively as follows: Level one consists of all open and closed subsets of R, and upon ...

The great success mathematicians had studying hypergeometric functions _pF_q(a_1,...,a_p;b_1,...,b_q;z) for the convergent cases (p<=q+1) prompted attempts to provide ...

Every bounded infinite set in R^n has an accumulation point. For n=1, an infinite subset of a closed bounded set S has an accumulation point in S. For instance, given a ...

Let M be a Riemannian manifold, and let the topological metric on M be defined by letting the distance between two points be the infimum of the lengths of curves joining the ...

A set in a Polish space is a Borel set iff it is both analytic and coanalytic. For subsets of w, a set is delta_1^1 iff it is "hyperarithmetic."