  The aim of this article is to provide characterizations for
subadditivity-like growth conditions for the so-called associated weight
functions in terms of the defning weight sequence. Such growth requirements
arise frequently in the literature and are standard when dealing with
ultradifferentiable function classes defned by Braun-Meise-Taylor weight
functions since they imply or even characterize important and desired
consequences for the underlying function spaces, e.g. closedness under
composition.
