On the Lebesgue Decomposition of the Multidimensional Infinitely Divisible Distributions

Abstract:

      In this paper we have investigated and proved various Lebesgue properties of the n-dimensional quasi-distributions. 2-dimensional quasi-distributions have been classified into 5 types. It is proved among others that every 2-dimensional quasi-distribution can be expressed uniquely as a sum of 5 functions belonging to different types. Some necessary and sufficient conditions for functions belonging to each given type have been analysed in detail.