Folklore in Multi-Objective Optimisation

In this paper, we present and prove some results in multi-objective optimisation that are considered folklore. For the most part, proofs for these results exist in special cases, but they are used in more general settings since their proofs can be (largely) transferred. We do this transfer explicitly and try to state the results as generally as possible. In particular, we also aim at providing clean and complete proofs for results where the original papers are not rigorous.