New York Journal of Mathematics
Volume 14 (2008) 235-259


G. R. Pantsulaia

On generators of shy sets on Polish topological vector spaces

Published: June 24, 2008
Keywords: Shy set, generator of shy set, Polish topological vector space
Subject: Primary 28Axx, 28Cxx, 28Dxx; Secondary 28C20, 28D10, 28D99

We introduce the notion of generators of shy sets in Polish topological vector spaces and give their various interesting applications. In particular, we demonstrate that this class contains specific measures which naturally generate implicitly introduced subclasses of shy sets. Moreover, such measures (unlike σ-finite Borel measures) possess many interesting, sometimes unexpected, geometric properties.

Author information

Department of Mathematics, Georgian Technical University, 77 Kostava St. 0175 Tbilisi 75, Georgia