Abstract
In this chapter we discuss a well-known family of theorems, known as Riesz Representation Theorems, that assert that positive linear functionals on classical normed Riesz space C(X) of continuous real functions on X can be represented as integrals with respect to Borel measures. To make sure everything is integrable, we restrict attention either to continuous functions with compact support, C c(X) and measures that are finite on compact sets, or to finite measures and bounded continuous functions, C b(X). We also consider positive functionals on the spaces of bounded measurable real functions B b (X).
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