Noun
Borel set (plural Borel sets)
(mathematical analysis) Any of the members of a Borel σ-algebra.
A Lebesgue measurable set is expressible as a union of a Borel set and a Lebesgue null set.
For instance, a real-valued measurable function is a function for which the preimage of each Borel set is measurable. Source: Internet
Halmos rather confusingly uses the term "Borel set" for elements of the σ-ring generated by compact sets, and defines Haar measure on these sets. Source: Internet
Indeed, for a Borel set S, let us denote by the set of inverses of elements of S. If we define : then this is a right Haar measure. Source: Internet
In 2010 Calvin Borel set a new record, being the first jockey to win 3 out of 4 consecutive Kentucky Derbys. citation Traditions In addition to the race itself, a number of traditions play a large role in the Derby atmosphere. Source: Internet
While the Cantor Set is a Borel set, has measure zero, and its power set has cardinality strictly greater than that of the reals. Source: Internet