ABSTRACT
This chapter is devoted to a comparative study of a measure and an analogous capacity function. The main result is a proof of Choquet’s fundamental theorem on the capacitability of analytic sets. This chapter enables a unification of various points of view and helps in further developments of the theory. It discusses the preliminaries on the analytic sets along with definitions as well as theorems and proofs. The work on analytic sets will be used in a calculation of certain “sizes”, analogous to (but distinct from) the outer measure studies. This function is called a capacity, and there are important nonmeasurable sets (for a Radon measure) in a topological space which are capacitable. The chapter is also devoted to an application of the capacity theorem in deducing the central results and some consequences of Daniell’s integration.
