This text contains my lecture notes for the graduate course “Weak Convergence” given in September-October 2013 and then in March-May 2015. The course is based on the book Convergence of Probability Measures by Patrick Billingsley, partially covering Chapters 1-3, 5-9, 12-14, 16, as well as appendices. In this text the formula label (∗) operates locally. The visible theorem labels often show the...

The first part of the paper deals with general features of weak star convergence from a topological point of view. We present basic facts about weak and weak star topologies, dual spaces and representations of linear functionals as Radon measures. A special attention is payed to finitely additive measures and some results regarding the Baire sets. We prove that in a wide class of topological sp...