Abstract
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≥2; 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.
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