On the models of Indlekofer and Kubilius in probabilistic number theory

Abstract. In his book [7] J. Kubilius constructed a finite probability space adapted for the investigation of additive functions. K.–H. Indlekofer presented in his articles [3], [4] a new method to investigate number theoretical questions with the help of probability theory. In this paper we describe the (finite) probability model of Kubilius and the model of Indlekofer which is based on the Stone–Čech compactification of \(\mathbb N\).