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473(1): 現代数学の系譜 工学物理雑談 古典ガロア理論も読む 2017/11/06(月)00:08 ID:1Au30FRy(7/13) AAS
>>472 つづき

先に私の見解を書いておくが、ピエロくんの紹介してくれた >>312 PDF が参考になるね（＾＾
The Mathematics of Coordinated Inference: A Study of Generalized Hat Problems (Developments in Mathematics) 2013 edition by Hardin, Christopher S., Taylor, Alan D.

これで、上記とちょっと違って、７章”The Topological Setting”とかなっていて、さすがに上記は、まずいということらしい。（＾＾

例えば、

P9
”In Chapter 7 we start to move further away from the hat problem
metaphor and think instead of trying to predict a function's value at a
point based on knowing (something about) its values on nearby points. The
most natural setting for this is a topological space and if we wanted to
only consider continuous colorings, then the limit operator would serve as
a unique optimal predictor. But we want to consider arbitrary colorings.
Thus we have each point in a topological space representing an agent and
if f and g are two colorings, then f ≡a g if f and g agree on some deleted
neighborhood of the point a. It turns out that an optimal predictor in this
case is wrong only on a set that is "scattered" (a concept with origins going
back to Cantor). Moreover, this predictor again turns out to be essentially
unique, and this is the main result in Chapter 8.”

などとある

さすれば、時枝もそのままじゃ（Topologicalな条件を加えないと）、成り立たないと思うがどう？（＾＾

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479: 2017/11/06(月)06:57 ID:7zpRwxYO(4/9) AAS
>>473
やれやれ不勉強な奴に限って目次だけで妄想するｗ

”The Topological Setting”は（無限帽子問題の）位相的バージョンくらいの意味
測度論的設定にたいして位相的設定も可能、ということだろ

本文読めよ　タコ

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