The theory of the strict
topology β on C∗(X) has recently been extended to a completely regular setting by
Sentilles. Here it is shown that equality of the separable and τ-additive Baire
measures on X is a sufficient condition for (C∗(X),β) to be a strong Mackey space.
As a consequence, the Conway-LeCam Theorem for paracompact spaces is
extended to the completely regular case. A locally convex topology βe on
C∗(X) is considered; βe is strong Mackey, and the dual space is the space
of separable measures. Results of Dudley, Granirer, and Leger and Soury
on convergence in the space of measures are unified and extended in this
context.
