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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Dubins–Spanier theorems ： ウィキペディア英語版 Dubins–Spanier theorems The Dubins–Spanier theorems are several theorems in the theory of fair cake-cutting. They were published by Lester Dubins and Edwin Spanier in 1961. Although the original motivation for these theorems is fair division, they are in fact general theorems in measure theory. == Setting == There is a set $U$, and a set $\backslash mathbb$ which is a sigma-algebra of subsets of $U$. There are $n$ partners. Every partner $i$ has a subjective value measure $V\_i:\; \backslash mathbb\; \backslash to\; \backslash mathbb$. This function determines how much each subset of $U$ is worth to that partner. Let $X$ a partition of $U$ to $k$ measurable sets: $U\; =\; X\_1\; \backslash sqcup\; \backslash cdots\; \backslash sqcup\; X\_k$. Define the matrix $M\_X$ as the following $n\backslash times\; k$ matrix: :$M\_X()\; =\; V\_i(X\_j)$ This matrix contains the valuations of all players to all pieces of the partition. Let $\backslash mathbb$ be the collection of all such matrices (for the same value measures, the same $k$, and different partitions): :$\backslash mathbb\; =\; \backslash$ The Dubins–Spanier theorems deal with the topological properties of $\backslash mathbb$. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Dubins–Spanier theorems」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.