Measures and all that --- A Tutorial (1409.2662v3)

Abstract: This tutorial gives an overview of some of the basic techniques of measure theory. It includes a study of Borel sets and their generators for Polish and for analytic spaces, the weak topology on the space of all finite positive measures including its metrics, as well as measurable selections. Integration is covered, and product measures are introduced, both for finite and for arbitrary factors, with an application to projective systems. Finally, the duals of the Lp-spaces are discussed, together with the Radon-Nikodym Theorem and the Riesz Representation Theorem. Case studies include applications to stochastic Kripke models, to bisimulations, and to quotients for transition kernels.