| 11. | Although any continuous preimage of a Borel set is Borel, not all analytic sets are Borel sets.
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| 12. | One way to do this is to define a measure on the Borel sets of the topological space.
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| 13. | Baire sets avoid some pathological properties of Borel sets on spaces without a countable base for the topology.
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| 14. | It is not-finite, as not every Borel set is at most a countable union of finite sets.
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| 15. | For example, all Borel sets of a Polish space have the property of Baire and the perfect set property.
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| 16. | One common use of the Borel hierarchy is to prove facts about the Borel sets using transfinite induction on rank.
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| 17. | To denote the number of points of { N } located in some Borel set B, it is sometimes written
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| 18. | It was shown in 1975 by Donald A . Martin that games whose winning set is a Borel set are determined.
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| 19. | A code for a lightface Borel set gives complete information about how to recover the set from sets of smaller rank.
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| 20. | In relation to a Borel set " B " the intensity measure of { N } is defined as:
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