Noun
Borel measure (plural Borel measures)
(mathematical analysis) A measure whose domain is the Borel σ-algebra of a locally compact Hausdorff space.
A subset of the Cantor set which is not Borel measurable The Borel measure is not complete. Source: Internet
It is also the completion of the Borel measure, as in the one-dimensional case. Source: Internet
Note that a locally finite Borel measure automatically satisfies μ(C) < ∞ for every compact set C. On the real line The real line with its usual topology is a locally compact Hausdorff space, hence we can define a Borel measure on it. Source: Internet
Region of convergence If f is a locally integrable function (or more generally a Borel measure locally of bounded variation), then the Laplace transform F(s) of f converges provided that the limit : exists. Source: Internet
The first chapter develops the theory of measure (see Borel measure ). Source: Internet