Independence, Additivity, Uncertainty

This book deals with the important economic problem of uncertainty. The first attempt was to simplify and unify some results usually taught in courses in mathematical economics. The economic interpretation of the results was representations of preferences as sums or integrals and the decomposition of preferences into utilities and probabilities. The book contains all the classical results, but the main justification of the book is that the approach taken in the earlier versions was also the proper approach in generalizing from preferences, which were total preorders to preferences, which were not total or transitive. The same mathematics gives representations which are additive. It also gives decompositions where concepts of utility, probability, and uncertainty appeared. These results are new and give a solution to how uncertainty can be formalized.