Converse of the Eilers-Horst theorem
The theorem of \textit{M. Eilers}, \textit{E. Horst} [Int. J. Theor. Phys. 13, 419-424 (1975; Zbl 0345.46021)] is generalized showing that any finite as well as any \(\sigma\)-finite measure on a quantum logic of a Hilbert space H is a Gleason one iff the dimension of H is a nonmeasurable cardinal \(\neq 2\).
\(\sigma \)-finite measure on a quantum logic
scientific article; zbMATH DE number 4026152