borel set in a sentence

Examples

1. Although any continuous preimage of a Borel set is Borel, not all analytic sets are Borel sets.
2. One way to do this is to define a measure on the Borel sets of the topological space.
3. Baire sets avoid some pathological properties of Borel sets on spaces without a countable base for the topology.
4. It is not-finite, as not every Borel set is at most a countable union of finite sets.
5. For example, all Borel sets of a Polish space have the property of Baire and the perfect set property.
6. One common use of the Borel hierarchy is to prove facts about the Borel sets using transfinite induction on rank.
7. To denote the number of points of { N } located in some Borel set B, it is sometimes written
8. It was shown in 1975 by Donald A . Martin that games whose winning set is a Borel set are determined.
9. A code for a lightface Borel set gives complete information about how to recover the set from sets of smaller rank.
10. In relation to a Borel set " B " the intensity measure of { N } is defined as: