On the measurability of orbits in Borel actions

Miller, Douglas E.

doi:10.1090/S0002-9939-1977-0440519-8

On the measurability of orbits in Borel actions
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Proc. Amer. Math. Soc. 63 (1977), 165-170 Request permission

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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