Theorem on the general form of a linear continuous functional in the space of continuous finite functions

Measure theory plays an important role in the theory of subharmonic and -subharmonic functions. The classical properties of a measure have been presented in many monographs, for example, in [1]. In the article we sharpen Azarin’s variant of the theorem on the general form of a linear continuous functional in the complex space of continuous compactly supported functions. The results of our article allow us to simplify the constructions from these articles somewhat.