RAMSEY FUNCTIONS FOR SYMMETRIC SUBSETS IN COMPACT ABELIAN GROUPS

Given a compact group G and r is an element of N, let s(r)(G) denote the least upper bound of real epsilon > 0 such that for every measurable r-coloring of G, there exists a monochrome symmetric subset of measure >= epsilon. A subset A subset of G is symmetric if there exists g is an element of G such that gA(-1) g = A. We give a general picture of asymptotic behaviour of the function s(r)(G) for compact Abelian groups.