On the measurability of orbits in Borel actions

Abstract

We replace measure with category in an argument of G. W. Mackey to characterize closed subgroups <italic>H</italic> of a totally nonmeager, 2nd countable topological group <italic>G</italic> in terms of the quotient Borel structure <italic>G/H</italic> . 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.