Integrable Measures

In this chapter, the authors define integrable measures with values in a Neumann space. They characterize integrable measures with the help of regularizations. The authors also define space of integrable measures. An example of a non-integrable measure is the Dirac mass. Uniformly continuous functions vanishing outside of a bounded set are integrable measures. The authors integrate “integrable measures”, which are equivalent to “classes of integrable functions which are a.e. equals” when E is a Frechet space. More precisely, they associate the measure f with a class f, where f(u) is the integral of fu for any test function u.