Titlebook: Independence, Additivity, Uncertainty; Karl Vind Book 2003 Springer-Verlag Berlin Heidelberg 2003 Keynes.Knight.Preferences.Uncertainty.Ut

Offbeat

Totally preordered setseordered sets and subsets of the real numbers. Some topological concepts are introduced in section 2.3 page 18. A total order gives rise to a topology and the main results from section 2.2 are in section 2.4 given in topological terms.

obtuse

仇恨

Mean groupoids operation o on .. Intuitively a o . can be thought of as the mean of or the midpoint between a and ., . o . = ., and if . ≻ ., then . ≻ . o . ≻ .. Later chapters will be concerned with totally preordered sets that have enough structure to define a mean operation on ((.,~),.).

follicle

ALB

Preferences and preference functionsChapter 2 treats totally ordered sets and gives representation theorems. Similar theorems for just relations — not assumed to be total — are trivial, but are convenient to have, because the main results in this book give conditions for particular additive representation.

FAST

Coronary-Spasm

folliculitis

PACK

A general integral representation by Birgit GrodalChapter 8 studied a totally preordered set . of functions . : . → ., where (.) is a measurable set and . an arbitrary set. . was under an independence condition shown to be a commutative mean groupoid..

Collision

Special integral representations by Birgit GrodalIn chapter 11 we gave conditions on . which implied the existence of a measurable function.