スレタイ 箱入り無数目を語る部屋29(あほ二人の”アナグマの姿焼き"Part3ｗ) (256ﾚｽ)
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4(5): 01/15(水)11:20 ID:ZCTGHyhi(4/19) AA×

外部ﾘﾝｸ:mathoverflow.net
外部ﾘﾝｸ[html]:alexanderpruss.blogspot.com

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4: [] 2025/01/15(水) 11:20:33.09 ID:ZCTGHyhi つづき https://mathoverflow.net/questions/151286/probabilities-in-a-riddle-involving-axiom-of-choice Probabilities in a riddle involving axiom of choice asked Dec 9 '13 at 16:16 Denis （Denis質問） I think it is ok, because the only probability measure we need is uniform probability on {0,1,…,N?1}, but other people argue it's not ok, because we would need to define a measure on sequences, and moreover axiom of choice messes everything up. （Pruss氏） The probabilistic reasoning depends on a conglomerability assumption, ・・・and we have no reason to think that the conglomerability assumption is appropriate. （Huynh氏） If it were somehow possible to put a 'uniform' measure on the space of all outcomes, then indeed one could guess correctly with arbitrarily high precision, but such a measure doesn't exist. mathoverflowは時枝類似で ・Denis質問でも、もともと”but other people argue it's not ok, because we would need to define a measure on sequences, and moreover axiom of choice messes everything up.” 　Denisの経歴で、彼は欧州の研究所勤務で、other peopleは研究所の確率に詳しいらしい ・Pruss氏とHuynh氏とは、経歴を見ると、数学DRです。両者とも、このパズル（＝riddle）は、可測性が保証されていないと回答しています なお ”試しに"Alex Pruss Conglomerability"で検索した結果 Alexander Pruss本人のBlogが見つかった”スレ25 414-415 https://alexanderpruss.blogspot.com/2024/09/independence-conglomerability.html Alexander Pruss's Blog September 11, 2024 Independence conglomerability Conglomerability says that if you have an event E and a partition {Ri : i ∈ I} of the probability space, then if P(E∣Ri) ≥ λ for all i, we likewise have P(E) ≥ λ. Conglomerabilityとは、ある事象Eと確率空間の分割{Ri:i∈I} があるとき、 すべてのi に対してP(E∣Ri) ≥λならば、同様にP(E) ≥λ が成り立つというものである。 Example: I am going to uniformly randomly choose a positive integer (using a countably infinite fair lottery, assuming for the sake of argument such is possible). For each positive integer n, you have a game available to you: the game is one you win if n is no less than the number I am going to pick. You despair: there is no way for you to have any chance to win, because whatever positive integer n you choose, I am infinitely more likely to get a number bigger than n than a number less than or equal to n, so the chance of you winning is zero or infinitesimal regardless which game you pick. つづく http://rio2016.5ch.net/test/read.cgi/math/1736907570/4
つづき 質問 氏 氏 は時枝類似で 質問でももともと の経歴で彼は欧州の研究所勤務で は研究所の確率に詳しいらしい 氏と氏とは経歴を見ると数学です両者ともこのパズルは可測性が保証されていないと回答しています なお 試しに で検索した結果 本人のが見つかったスレ とはある事象と確率空間の分割 があるとき すべての に対して ならば同様に が成り立つというものである つづく

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