Independence, Additivity, Uncertainty

• 1 Introduction.- 1.1 Economics.- 1.2 Statistics.- 1.3 Mathematic.- 1.4 Summary of results.- 1.5 Applications.- I Basic Mathematics.- 2 Totally preordered sets.- 3 Preferences and preference functions.- 4 Totally preordered product sets.- 5 A subset of a product set.- 6 Mean groupoids.- 7 Products of two sets as a mean groupoid.- II Relations on Function Spaces.- 8 Totally preordered function spaces.- 9 Relations on function spaces.- III Relations on Measures.- 10 Relations on sets of probability measures.- IV Integral Representations.- 11 A general integral representation by Birgit Grodal.- 12 Special integral representations by Birgit Grodal.- V Decompositions and Uncertainty.- 13 Decompositions. Uncertainty.- 14 Uncertainty on products.- 15 Conditional uncertainty.- VI Applications.- 16 Production, utility, preference.- 17 Preferences over time.- 18 A foundation for statistics.- References.

From the reviews of the first edition: "The most important contribution of this book is to formalize, simplify and unify concepts of uncertainity that occur in mathematical economics. ... This well-written book provides an elegant and serious introduction to the basic concepts and results of representations of preferences as sums and integrals. It discusses in detail the decomposition of preferences into utilities and probabilities. This lively presentation ... is impressive. The book will serve as an inspiration for further research and can be recommended ... ." (P.R. Parthasarathy, Zentralblatt MATH, Vol. 1080, 2006)