Distribution of values of certain classes of additive arithmetic functions in algebraic number fields

An investigation is made of the generalization of a theorem of B. V. Levin and A. S. Fainleib for homothetically extending regions in a certain $n$-dimensional real space connected with a given field $K$ of algebraic numbers of degree $n\ge2$; the paper also investigates applications of the theorem to the problem of the distribution of real additive functions which are given on a set of ideal numbers and which belong to a wider class than the class $H$ of I. P. Kubilyus.