In [1,2,3], A. C. Baker and J.W. Baker studied the subspace Ma(S) of the
convolution measure algebra M, (S) of a locally compact semigroup. H.
Dzinotyiweyi in [5,7] considers an analogous measure space on a large class
of C-distinguished topological semigroups containing all completely regular
topological semigroups. In this paper, we extend the definitions to study the
weighted semigroup algebra Ma (S, o), where o is a weight function on a Cdistinguished
semitopological semigroup S. We will show that this subspace
is a convolution measure algebra. As acorollary, this answers in the affirmative
a question raised by J.W. Baker and H. Dzinotyiweyi in [6]