medium size jobs. For that reason we will use the same classification of jobs that is based on the following lemma. As Das and Wiese also gave a very short and nice proof by contradiction, we will omit the proof in this paper and refer to [@bagptas].

\[lem:medk\] We can compute $k \in \mathbb{N}_{\le \frac{1}{\epsilon^2}}$ such that $\sum\limits_{j\in J : p_j \in [\epsilon^{k+1},\epsilon^{k})}{p_j} \le \epsilon^2 *m$.

For the rest of this paper we will assume that $k$ is set to be the parameter of this lemma. We will further classify jobs just like in [@bagptas] with this $k$ as follows: We call a job $j$ *large* if $p_j \ge \epsilon^k$, *medium* if $\epsilon^k > p_j \ge \epsilon^{k+1} $ and *small* if $p_j < \epsilon^{k+1}$. Finally we also want to respect bags that have a large amount of medium and large jobs. We call a bag $B_l$ *large* when $B_l$ holds at least $\epsilon *m$ jobs that are medium or large. If a bag is not large we call it *small*. We can also note that the amount of large bags is bounded by $O(\frac{1}{\epsilon^{k+2}})$ [@bagptas].

For our EPTAS we will need another type of bag-classification. To be able to schedule 