On Drewnowski lemma for non-additive functions and its consequences

Abstract

In this paper we state an extension of a Drewnowski lemma to non-additive functions which are defined on an orthomodular structure and attain values into a uniform space, where no algebraic structure is required and the uniformity is induced by a complete metric. As consequences we prove Brooks–Jewett as well as Cafiero theorems for such class of functions

Dieudonné's theorem for non-additive set functions

“…A straightforward consequence of the previous criterion is the following: We remember that in [7] we have a generalizations of Brooks-Jewett Theorem for quasi-triangular functions (see also [18,Theorem 12.4], where the theorem is proved for particular non-additive functions defined in a D-poset). This is a particular case of Corollary 4.2, when R = G.…”