A linear ordering theorem for weighted means of functions relative to weight functions

The aim of this article is to continue to develop the theory of generalized weighted means of functions relative to weight functions in Euclidean n-space (Glaser, 1990) by proving a generalization of the one-dimensional Cashwell-Everett linear ordering theorem (Cashwell-Everett (1969). These generalized means lie in an n-dimensional cone which shrinks down to a line for the special case n = 1. This theorem has many interesting consequences which could be the subject of future articles.