On topologically invariant means on a locally compact group

Let M be the set of all probability measures on βN. Let G be a locally compact, noncompact, amenable group. Then there is a one-one affine mapping of M into the set of all left invariant means on L^∞(G). Note that M is a very big set. If we further assume G to be a-compact, then we have a better result: The set Jl can be embedded affinely into the set of two-sided topologically invariant means onL^∞(G). We also give a structure theorem for the set of all topologically left invariant means when G is σ-compact.