When is an invariant mean the limit of a Følner net? (Q2049870)

The author deals with the topological invariant mean on \(G\), say \(TLIM(G)\), and the limit points of Følner-nets, say \(TLIM_{0}(G)\), where \(G\) is an amenable locally compact group. The author also discusses whether \(TLIM(G)=TLIM_{0}(G)\). Using these facts some previous results like [\textit{C. Chou}, Trans. Am. Math. Soc. 151, 443--456 (1970; Zbl 0202.14001)] and [\textit{N. Hindman} and \textit{D. Strauss}, Topology Appl. 156, No. 16, 2614--2628 (2009; Zbl 1189.22003)] are improved.