in this paper, a local approach to the concept of hudetz $g$-entropy is presented. the introduced concept is stated in terms of hudetz $g$-entropy. this representation is based on the concept of $g$-ergodic decomposition which is a result of the choquet's representation theorem for compact convex metrizable subsets of locally convex spaces.

fi = inf( p(x) : g(x) E 4, x E R 1, P) where S is an arbitrary convex cone in a finite dimensional space, R is a convex set, and p and g are respectively convex and S-convex (on a), were given in [lo]. These characterizations hold without any constraint qualification. They use the “minimal cone” .S’ of (P) and the cone of directions of constancy D;(S’). In the faithfully convex case these cones...

Tom Richmond* ([email protected]). Complementation in the Lattice of Locally Convex Topologies. We find all locally convex homogeneous topologies on (R,≤) and determine which of these have locally convex complements. Among the locally convex topologies on a n-point totally ordered set, each has a locally convex complement, and at least n of them have 2n−1 locally convex complements. For any ...

This paper develops inferential theory for hypothesis testing under general convex cone alternatives for correlated data. Often, interest lies in detecting order among treatment effects, while simultaneously modeling relationships with regression parameters. Incorporating shape or order restrictions in the modeling framework improves the efficiency of statistical methods. While there exists ext...