More on the locally convex space (M(X), β(X)) of a locally compact Hausdorff space X

In the previous paper [12] we introduced the definition of the strict topology beta(X) on the measure space M(X) for a locally compact Hausdorff space X. In this paper, we consider on M(X) the topology beta(X) and we show that beta(X) is the weak topology under all left multipliers induced by a function space on M(X). We then show that beta(X) can be considered as a mixed topology. This result is not only of interest in its own right, but also it paves the way to prove that (M(X), beta(X)) is a Mazur space and the locally convex space (M(S), beta(S)), equipped with the convolution multiplication is a complete semitopological algebra, for a wide class of locally compact semi groups S.