Theorem on the representation measures

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]. It is known that any real measure can be represented in the form of Hahn and Jordan. In the article we sharpen Hahn’s and Jordan’s variant. The results of our article allow us to simplify the constructions from these articles somewhat.