We give a characterization of the family of all probability measures on the extended line $(-\infty,+\infty]$, which may be obtained as the distribution of the maximum of some linear Bernoulli process.
"A note on the distributions of the maximum of linear Bernoulli processes." Electron. Commun. Probab. 13 266 - 271, 2008. https://doi.org/10.1214/ECP.v13-1375