Offbeat
发表于 2025-3-23 10:40:56
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
发表于 2025-3-23 17:55:48
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仇恨
发表于 2025-3-23 21:16:06
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
发表于 2025-3-23 22:20:32
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ALB
发表于 2025-3-24 04:03:19
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
发表于 2025-3-24 10:36:26
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Coronary-Spasm
发表于 2025-3-24 11:56:37
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folliculitis
发表于 2025-3-24 17:11:42
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PACK
发表于 2025-3-24 20:23:16
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
发表于 2025-3-25 01:49:00
Special integral representations by Birgit GrodalIn chapter 11 we gave conditions on . which implied the existence of a measurable function.