Weakly dense subsets of the measure algebra

Abstract

We introduce the notion of the weak density of a Boolean algebra and show that for homogeneous measure algebras it coincides with the density (=least size of a coinitial set). From this we obtain a partial lifting of the measure algebra of [ 0 , 1 ] \left [ {0,1} \right ] of minimal size which does not extend to a lifting. It also follows that the π \pi -character of each point and the π \pi -weight are the same for the Stone space of a homogeneous measure algebra