An approach to determining the existence of a limit distribution of additive arithmetic functions

An approach will be proposed to determine the existence of a limit distribution of additive arithmetic functions in this work. It is based on assertions that will be proven in this work and on the properties of Dirichlet convolution and Möbius inversion. Based on this approach, formulas will be obtained for finding the mean and variance for the limit distribution of additive arithmetic functions. Examples of this approach to proving the existence of a limit distribution of additive arithmetic functions and finding the mean value and variance for the limit distribution of additive arithmetic functions are considered.