Descriptive Set Theory

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4 domain-specific abstractions whose origin domain is Descriptive Set Theory.

• Baire function — A real-valued function obtainable from continuous functions by countable transfinite iteration of pointwise sequential limits, classified by the least countable ordinal stage required.
• Property of Baire — The property of a set that it differs from some open set by a meager set.
• Standard Borel space — A measurable space isomorphic to the Borel measurable space of a Polish space, providing a regular setting in which measurable bijections and probability constructions behave well.
• Universally measurable set — A subset of a Polish space measurable in the completion of every finite Borel measure on that space.