ABSTRACT
This chapter is devoted to an introduction to measures on Hausdorff topological spaces. After discussing the regularity properties of a measure on such a general space, it shows that a Radon measure is strictly localizable, and the remaining work is largely for Borel measures on locally compact spaces. The chapter gives two proofs of the classical Riesz-Markov theorem for linear functionals on a continuous function space. It includes a treatment of the existence of a (left) Haar measure on a locally compact group and extensions of measures on lattices based on general topological space. The chapter presents background and preliminaries of the topological measures along with the definitions as well as theorems and proofs. It also includes multiple exercises that help students try themselves and perform topological measures.
