On obeying constraints of asymptotic character

We consider an abstract attainability problem under constraints of asymptotic character and describe a general approach to constructing “nonsequential” attraction sets in the space of generalized elements formalized as finitely additive measures. We also study the existence and structure of an asymptotic formula universal in the range of “asymptotic constraints” and topologies of the space of generalized elements in the case when the space of ordinary solutions is not necessarily compactifiable.