Chapter 4: Clunie and Mohon'ko type theorems

In this chapter, we prove tropical counterparts to three lemmas from classical complex analysis, frequently used in applications of Nevanlinna theory. As to these classical results, the reader may look at a lemma due to Valiron and Mohon'ko, see [68], Theorem 2.2.5, another one due to Mohon'ko, see [68], Proposition 9.2.3, and the original Clunie lemma in [18]. Previous tropical versions for these lemmas may be found in [46], [71] and [69]. The first two of these references are treating the restricted case of integer slopes only.