ON VOLUME TYPE FUNCTIONALS IN EUCLIDEAN GEOMETRY - Kirtadze, Aleks (Annual of Sofia University St. Kliment Ohridski. Faculty of Mathematics and Informatics, 2016)
The paper is concerned with some aspects of the theory of volumes in Euclidean space. In this context, it is shown that there exists a solution of Cauchy’s functional equation, which is absolutely nonmeasurable with respect to the class of all translation invariant measures on the real line $R$, extending the Lebesgue measure on $R$.