Kominek, Z.; Reich, L.; Schwaiger, J. On additive functions fulfilling some additional condition. (English) Zbl 1046.39019 Sitzungsber., Abt. II, Österr. Akad. Wiss., Math.-Naturwiss. Kl. 207, 35-42 (1998). The authors give a positive answer to a generalization of a question asked by G. Szabó [Aequationes Math. 46, 294 (1993)] at the 30th International Symposium on Functional Equations (Oberwolfach, 1992): Let \(D\) be a subset of positive Lebesgue measure of \(\mathbb{R}^{2n}.\) Then any additive function \(f:\mathbb{R}^n\to\mathbb{R}\) satisfying \((x,y)\in D\Rightarrow f(x)f(y)=0\) has to be identically 0. Further generalizations are also offered. Reviewer: János Aczél (Waterloo/Ontario) Cited in 1 ReviewCited in 4 Documents MSC: 39B22 Functional equations for real functions 39B55 Orthogonal additivity and other conditional functional equations Keywords:conditional Cauchy equations; additive functions PDFBibTeX XMLCite \textit{Z. Kominek} et al., Sitzungsber., Abt. II, Österr. Akad. Wiss., Math.-Naturwiss. Kl. 207, 35--42 (1998; Zbl 1046.39019)