In 2010 Calvin Borel set a new record, being the first jockey to win 3 out of 4 consecutive Kentucky Derbys.
22.
The Borel sets in the following statement refer to the ?-algebra generated by the " open " sets.
23.
It follows easily from this characterization of propositions in classical systems that the corresponding logic is identical to that of some Borel sets.
24.
Let the counting measure,, of a Borel set be defined as the number of elements of if is finite, and otherwise.
25.
The measurable sets on the line are iterated countable unions and intersections of intervals ( called Borel sets ) plus-minus null sets.
26.
Since every open set is almost open ( the empty set is meager ), it follows that every Borel set is almost open.
27.
Alternatively, the number of points of \ textstyle { N } located in some Borel set \ textstyle B is often written as:
28.
In some contexts, Borel sets are defined to be generated by the compact sets of the topological space, rather than the open sets.
29.
In practice, the use of Baire measures on Baire sets can often be replaced by the use of regular Borel measures on Borel sets.
30.
Let X be a complete separable metric space and \ mathfrak { B } ( X ) the ?-algebra of its Borel sets.
