  Chapter 1 deals with the problem of the existence of an upper/lower envelope
from a convex cone or, more generally, a convex set for functions on the
projective limit of vector lattices with values in the completion of the
Kantorovich space or on the extended real line. Vector, ordinal and topological
dual interpretations of the existence conditions of such envelope and the
method of its construction are given. Chapter 2 presents applications to the
existence of a nontrivial (pluri)subharmonic and/or (pluri) harmonic minorant
for functions in domains from finite-dimensional real or complex space. General
approaches to the problems of nontriviality of weight classes of holomorphic
functions, to the description of zero (sub)sets for such classes of holomorphic
functions, to the problem of representation of a meromorphic function as a
ratio holomorphic functions from a given weight class are indicated.
