Borel globalizations of partial actions of Polish groups

摘要

We show that the enveloping space of a partial action of a Polish group G on a Polish space is a standard Borel space, that is to say, there is a topology on such that is Polish and the quotient Borel structure on is equal to . To prove this result we show a generalization of a theorem of Burgess about Borel selectors for the orbit equivalence relation induced by a group action and also show that some properties of the Vaught's transform are valid for partial actions of groups.