Approximate identities in spaces of all absolutely continuous measures on locally compact semigroups

Let G be a, locally compact group. Then M-a (G), the space of all absolutely continuous measures on G, has a bounded approximate identity [4]. Baker and Baker [1, 2] proved that (L) over tilde (S) (the space of all measures mu is an element of M(S) so that maps x bar right arrow epsilon(x) * \mu\ and x bar right arrow \mu\ * epsilon(x) are weak continuous from a locally compact semigroup S into M(S)) is closed under absolutely continuity and has all approximate identity. The main purpose of this paper is to show, that similar results hold true for a locally compact semigroup S and M-a(S) the space of all absolutely continuous measures on S.