Universally Measurable Set

(Descriptive Set Theory)

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Descriptive Set Theory
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What is Universally measurable set?

In mathematics, a subset of a Polish space is universally measurable if it is measurable with respect to every complete probability measure on that measures all Borel subsets of . In particular, a universally measurable set of reals is necessarily Lebesgue measurable (see below). Every analytic set is universally measurable. It follows from projective determinacy, which in turn follows from sufficient large cardinals, that every projective set is universally measurable.

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descriptive set theorydeterminacymeasure theory

Synonyms

Universally measurable

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