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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the extension property of measurable spaces


Authors: Włodzimierz Bzyl and Adam Mysior
Journal: Proc. Amer. Math. Soc. 92 (1984), 501-504
MSC: Primary 28A05; Secondary 03E15
MathSciNet review: 760933
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Abstract: We prove that a metrizable measurable space has the extension property if and only if it is isomorphic to a Borel subset of the real line. It follows, in particular, that $ ({\mathbf{R}},\mathcal{P}({\mathbf{R}}))$ does not have the extension property. Both results answer the questions raised by R. M. Shortt.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0760933-4
PII: S 0002-9939(1984)0760933-4
Keywords: Measurable space, extension property, standard space, metrizable measurable space, analytic set
Article copyright: © Copyright 1984 American Mathematical Society