EXTREME-POINTS OF A SET OF CONTENTS MAJORIZED BY A SUBMODULAR SET FUNCTION

The extreme points of the set of contents on an algebra A, which are majorized by a submodular set function u, have already been characterized for certain special cases (see [13], [4], [12]). The main result (Theorem 9) of this paper gives a characterization for the case that u is a simple submodular set function in the sense of Section 3. On the way, a decomposition property of these contents is obtained using the Summensatz from [10], and some results are proved for contents defined in terms of maximal filters.