About: Universally measurable set

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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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  • 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. (en)
  • 측도론에서, 가측 공간 위의 보편 완비 가측 공간(普遍完備可測空間, 영어: universally complete measurable space)은 모든 시그마 유한 완비화에 대하여 가측 집합이 되는 부분 집합들만을 가측 집합으로 삼는 가측 공간이다. (ko)
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  • 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. (en)
  • 측도론에서, 가측 공간 위의 보편 완비 가측 공간(普遍完備可測空間, 영어: universally complete measurable space)은 모든 시그마 유한 완비화에 대하여 가측 집합이 되는 부분 집합들만을 가측 집합으로 삼는 가측 공간이다. (ko)
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  • 보편 완비 가측 공간 (ko)
  • Universally measurable set (en)
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