4 research outputs found
Measures and all that --- A Tutorial
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