Totally monotone core and products of monotone

Several approaches to the product of non-additive monotone measures (or cap acities) are discussed and a new approach is proposed. It starts with the M obius product [E. Hendon, H.J. Jacobsen, B. Sloth, T. Tranaes, The product of capacities and belief functions, Mathematical Social Sciences 32 (1996) 95-108] of totally monotone measures and extends it by means of a supremum to general monotone measures. The sup runs over sets of totally monotone me asures. These sets are defined like the core of monotone measures (or coope rative games). The new product is compatible with the partial order less th an or equal to for arbitrary monotone measures. (C) 2000 Elsevier Science I nc. All rights reserved.