... absolute constants in O(·).In the recent decade, a lot of investigations were devoted to the limit distributions of values of additive functions with respect to νn. Given a real two dimensional ... result.The proposition is proved.3 Proofs of Theorems and CorollariesThe claim of Theorem 1 follows from Proposition 2. We will discuss only the remainingstatements.Proof of Corollary. The ... Pfeifer, On improvements of the order of approximation in thePoisson limit theorem, J. Appl. Probab., 1996, 33, 146–155 .[5] J M. De Koninck and G. Tenenbaum, Sur la loi de r´epartition du k-i`eme...