A generalization of Lévy's theorem on positive matrix semigroups

We generalize a fundamental theorem on positive matrix semigroups stating that each component is either strictly positive for all times or identically zero ("L & eacute;vy's Theorem"). Our proof of this fact that does not require the matrices to be continuous at time zero. We also provide a formulation of this theorem in the terminology of positive operator semigroups on sequence spaces.