A Daniell-Kolmogorov theorem for supremum preserving upper probabilities

Possibility measures are interpreted as upper probabilities that are in par ticular supremum preserving. We define a possibilistic process as a special family of possibilistic variables, and show how its possibility distributi on functions can be constructed. We introduce and study the notions of inne r and outer regularity for possibility measures. Using these notions, we pr ove an analogon for possibilistic processes (and possibility measures) of t he well-known probabilistic Daniell-Kolmogorov theorem, in the important sp ecial case that the variables assume values in compact spaces, and that the possibility measures involved are regular. (C) 1999 Elsevier Science B.V. All rights reserved.