On lattice-valued functions. I: Simple functions on lattice (Q2731755)

This is another one of a series of papers in which the authors develop their fuzzy measure and integration theory based on the concept of an ``\(x\)-lattice'' (defined by a complicated system of axioms). No examples are given which motivate this structure. (Reviewer's remark: It can be shown that an \(x\)-lattice satisfying an additional condition assumed in several theorems is isomorphic to \([0,+\infty]\)).NEWLINENEWLINENEWLINEIn the paper under review the authors give some elementary properties of simple functionsNEWLINENEWLINENEWLINE[See also the following review of Part II].