Radon Measures and Integral Representations

Abstract

It is well known that the pure set-theoretical theory of measure and integration has its limitations, and many interesting results need a topological frame because measure spaces without an underlying “nice” topological structure may be very pathological. In classical analysis this difficulty was overcome by introducing the theory of Radon measures on locally compact spaces. On these spaces there is a particularly important one-to-one relationship between Radon measures and certain linear functionals (see below) which in many treatments on analysis leads to the definition, that a Radon measure is a linear functional with certain properties.