Abstract
Establishing the structure of dense sum-free subsets of the torus group $\mathbb{R}/\mathbb{Z}$, we find an absolute constant $\alpha_0<1/3$ such that for any sum-free subset $A\subseteq\mathbb{R}/\mathbb{Z}$ with the inner measure $\mu(A)>\alpha_0$ there exists an integer $q\ge 1$ so that $$A \subseteq \bigcup_{j=0}^{q-1}[ \frac{j+\mu(A)}q, \frac{j+1-\mu(A)}q ].$$
Citation
Vsevolod F. Lev. "On sum-free subsets of the torus group." Funct. Approx. Comment. Math. 37 (2) 277 - 283, September 2007. https://doi.org/10.7169/facm/1229619653
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