On Extending Actions
Copyright policy )On Extending Actions
Consider a Polish topological group G G acting via J J on a substandard (= countably generated) Borel space. Theorem 1 . Any such "Borel action" can be extended to a Borel action J ′ : G × X ′ → X ′ J’:G \times X’ \to X’ where X ′ X’ is coanalytic. (Theorem 3 gives an analogue for continuous actions.) Corollary 2 . The result "in any Borel action, orbits are Borel" implies the (well-known) result "all such orbits are absolutely Borel" .
Borel space, Polish topological group, Borel action, Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets), Transformation groups and semigroups (topological aspects), coanalytic subset
Borel space, Polish topological group, Borel action, Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets), Transformation groups and semigroups (topological aspects), coanalytic subset
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).0 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!