Journal of Mathematical Sciences: Advances and ApplicationsAuthor's: GOGI R. PANTSULAIA
Pages: [61] - [78]
Received Date: Received August 16, 2012
Submitted by:
By using a technique of invariant measures developed by Oxtoby [11] for a Polish group, which is dense in itself, we prove an existence of a quasi-finite left (or right) invariant generator of left (or right)-shy sets in an entire group and establish that no any element of the class of all quasi-finite generators of left (or right)-shy sets possesses a uniqueness property. We get the validity of an analogous result for quasi-finite generators of two-sided-shy sets in Polish groups, which are dense in itself and are equipped with two-sided invariant metrics. These results allows us to answer to Questions 2.1-2.2 posed in [17].
Polish group, invariant measure, shy set, generator of shy sets.
