Contradiction in Conditions for Theorem for comparison of Markov Chains?

Question

In this paper ( here: https://epubs.siam.org/doi/pdf/10.1137/1122004 or here: https://www.tandfonline.com/doi/pdf/10.1080/02331887608801286?needAccess=true) by Kirstein, Franken and Stoyan, the theorem 4.2 states that one continuous time Markov chain with generator $Q_1=(q_{ij}^1)$ dominates in law another one with generator $Q_2=(q_{ij}^2)$, if $$ \sum_{l\geq k} q_{ml}^1\geq \sum_{l\geq k} q_{jl}^2$$ for all $j,m,k\in\mathbb{N}$ with $j\leq m,k>m,k\leq j$. (see equation 4.12 in the paper.) This condition does not make any sense, since it gives $k<k$, which is never satisfied. Does anyone have insights on this issue? What else could it mean?