Measure theory | Descriptive set theory | Determinacy

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. (Wikipedia).

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From playlist Set Theory by Mathoma

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From playlist Proofs

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From playlist Axiomatic Set Theory

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From playlist Set Theory

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From playlist Set Theory

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From playlist Set Theory

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From playlist Set Theory by Mathoma

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From playlist Determining the Domain and Range of a Function

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From playlist Proofs

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From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications

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From playlist 2018 - T2 - Measurement and Control of Quantum Systems: Theory and Experiments

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From playlist Workshop: Calculus of Variations in Probability and Geometry

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Listing Subsets Using Tree Diagrams | Set Theory, Subsets, Power Sets

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From playlist Set Theory

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From playlist PiTP 2017

Related pages

Borel set | Large cardinal | Complete measure | Analytic set | Mathematics | Real number | Polish space | Probability measure | Subset