Abstract. We show that a generalized form of the infimal convolution can be used to derive a dominated, monotone and additive extension theorem from the corresponding sandwich one on an abelian preordered semigroup with neutral element. Thus, we can put some of the results and arguments of Benno Fuchssteiner and Wolfgang Lusky into a proper perspective.

AMS Subject Classification (1991): 46A22, 06F05

Keyword(s): preordered semigroups, infimal convolutions, monotone additive functions, sandwich and extension theorems

Received June 18, 2009, and in revised form October 18, 2009. (Registered under 81/2009.)