We investigate whether Debreu's (Journal of Mathematical Economics, 1 (1974
) 15-23) decomposition can be used to characterize aggregate demand functio
ns f:R-++(2) --> R-+(2) on an arbitrary compact set K subset of R-++(2). It
is shown that in a special case a necessary condition obtained by Sonnensc
hein/Shafer and Koch will be sufficient. (C) 1999 Elsevier Science S.A. All
rights reserved.