When we discuss for a given function such properties as subadditivity, we may ask if the property holds for all possible values of the variables, or, if the answer to this first type of prob- lem turns out to be negative, we may ask if the properties hold "asymptotically", i.e., for values of the variable which are greater than a given value M (specified, if possible, or unspecified, if we do not have a choice).