LOWER PROBABILITIES AND FUNCTION REPRESENTATION

Supermodular functions can be represented as minima of suitable modula r functions under certain constraints. A general order-theoretic condi tion allowing such representations for functions on orders and lattice s respectively will be introduced. The underlying idea is redistributi on (movement) of ''mass'' given by the Mobius inverse of the function to be expressed. The representation of a (Choquet) capacity as a minim um of probability distributions - a so-called lower probability - is a n important special case.