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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On the measurability of orbits in Borel actions

Author: Douglas E. Miller
Journal: Proc. Amer. Math. Soc. 63 (1977), 165-170
MSC: Primary 54H15; Secondary 22A05
MathSciNet review: 0440519
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Abstract: We replace measure with category in an argument of G. W. Mackey to characterize closed subgroups H of a totally nonmeager, 2nd countable topological group G in terms of the quotient Borel structure G/H. As a corollary, we obtain an improved version of a theorem of C. Ryll-Nardzewski on the Borel measurability of orbits in continuous actions by Polish groups.

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Keywords: Transformation group, orbit, Baire space, Polish group, totally nonmeager, Borel action, countably separated Borel space, zero-one law, selector
Article copyright: © Copyright 1977 American Mathematical Society

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