Let J( be the set of all probability measures on ßN. Let G be a locally compact, noncompact, amenable group. Then there is a one-one affine mapping of J( into the set of all left invariant means on L"(G). Note that Jt is a very big set. If we further assume G to be a-compact, then we have a better result : The set Jt can be embedded affinely into the set of two-sided topologically invariant means on L"(G). We also give a structure theorem for the set of all topologically left invariant means… CONTINUE READING