Nontotal boundedness of the Fréchet–Nikodym space of a nonatomic quasi-measure
Bulletin Polish Acad. Sci. Math.
MSC: Primary 28A10; Secondary 54E25, 54E35, 05B40, 94B99
DOI: 10.4064/ba250612-13-3
Published online: 31 March 2026
Abstract
Let $A$ be a Boolean algebra and let $\mu $ be a nonatomic probability quasi-measure on $A$. Then there exists an infinite sequence $(a_n)$ in $A$ such that $\mu (a_i\vartriangle a_j) \gt \frac 12$ for all $i\neq j$. The constant $\frac 12$ is best possible. A similar problem concerning finite sequences in $A$ is also considered and its connection with the theory of binary codes is established.
