The aim of this book is to outline an elementary theory of linear func￾tionals on convex cones, but convex cones are here taken in a slightly more
general way than usual, they need not be imbedded in a vector space. In
consequence, we do not have a general cancellation law for the addition.
Typical examples for the cones we have in mind are 6 = R u I- -1 or the
upper semicontinuous 6- valued functions on some topological space.
Accordingly, linear functionals on such cones are allowed to attain values
in 6 instead of R . This generality has advantages with respect to
extensions of linear functionals.