Selected topics in convergence of measures on compact spaces

During my talk I'll present some most recent results of my joint work with Lyubomyr Zdomskyy concerning different aspects of convergence of sequences of Radon measures on compact spaces. Among others, I'll present a (sketch of a) constructive and elementary proof of the fact that the Banach space c_0 is always complemented in the space C(K\times L) of continuous functions on the product of any two infinite compact spaces K and L, as well as I'll show an example of a family of compact spaces K such that the space C(K) has the Grothendieck property for sequences of measures with countable supports, i.e. elements of ell_1(K), but not for sequences of measures with uncountable supports. If time allows, minimally generated Boolean algebras will appear, too.