| 1. | Any measure defined on the Borel sets is called a Borel measure.
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| 2. | Some authors define a Haar measure on Baire sets rather than Borel sets.
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| 3. | Note that the boldface hierarchy is just the standard hierarchy of Borel sets.
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| 4. | Classical descriptive set theory includes the study of regularity properties of Borel sets.
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| 5. | Each lightface Borel set has infinitely many distinct codes.
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| 6. | Just beyond the Borel sets in complexity are the analytic sets and coanalytic sets.
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| 7. | Every Baire set is a Borel set.
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| 8. | Borel sets and the associated Borel hierarchy also play a fundamental role in descriptive set theory.
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| 9. | The generalization to Borel sets is more involved, and requires the theory of Suslin sets.
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| 10. | Although any continuous preimage of a Borel set is Borel, not all analytic sets are Borel sets.
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