In page 123 of the book Markov Processes (Ethier Kurtz 1986, 2005)- convergence and characterization one reads
So far no problem, but when we turn to page 124 a few troubles appear:
Question 1 - What is the meaning of $\Gamma_{i/m_l}$
Question 2 - since $x'(t) = x\big(\frac{[m_i t]+1}{m_i}\big)$ the distance
$$r(x'(t), x(t)) \leq \frac{2}{l} $$ as long as $\frac{[m_i t]+1}{m_i} \in [t_i,t_{i+1})$ because we can use (6.9). However, since $t\leq\frac{[m_i t]+1}{m_i}\leq t + \delta_i$ how can we bound the distance of $r(x'(t), x(t)) $ for the cases when (by misfortune) $\frac{[m_i t]+1}{m_i} > t_{i+1}$?