[過去ﾛｸﾞ] 現代数学の系譜 工学物理雑談 古典ガロア理論も読む75 (1002ﾚｽ)

現代数学の系譜 工学物理雑談 古典ガロア理論も読む75 http://rio2016.5ch.net/test/read.cgi/math/1565872684/

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263: 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE [sage] 2019/08/17(土) 19:40:28.83 ID:sbItYGIt >>262 つづき （mathoverflowの”conglomerability”関連箇所） https://mathoverflow.net/questions/151286/probabilities-in-a-riddle-involving-axiom-of-choice Probabilities in a riddle involving axiom of choice Dec 9 '13 　(抜粋) （Alexander Pruss氏） ＜12＞ (抜粋) The probabilistic reasoning depends on a conglomerability assumption・・ But we have no reason to think the event of guessing correctly is measurable with respect to the probability measure induced by the random choice of sequence and index i, and we have no reason to think that the conglomerability assumption is appropriate. A quick way to see that the conglomerability assumption is going to be dubious is to consider the analogy of the Brown-Freiling argument against the Continuum Hypothesis (see here for a discussion). http://www.mdpi.com/2073-8994/3/3/636 (引用終り) 以上 http://rio2016.5ch.net/test/read.cgi/math/1565872684/263

301: 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE [sage] 2019/08/17(土) 22:13:47.15 ID:sbItYGIt >>263 補足 https://mathoverflow.net/questions/151286/probabilities-in-a-riddle-involving-axiom-of-choice Probabilities in a riddle involving axiom of choice Dec 9 '13 　(抜粋) （Alexander Pruss氏） ＜12＞ The probabilistic reasoning depends on a conglomerability assumption・・ But we have no reason to think the event of guessing correctly is measurable with respect to the probability measure induced by the random choice of sequence and index i, and we have no reason to think that the conglomerability assumption is appropriate. A quick way to see that the conglomerability assumption is going to be dubious is to consider the analogy of the Brown-Freiling argument against the Continuum Hypothesis (see here for a discussion). http://www.mdpi.com/2073-8994/3/3/636 (引用終り) かくいう私も、最初これを読んだとき、意味が取れなかった ”conglomerability”？ はて？ という感じで ”Brown-Freiling argument”も調べたが、いまいち分らなかった ところが、最近 >>262の下記を見つけてね。やっぱり、 ”But we have no reason to think the event of guessing correctly is measurable with respect to the probability measure induced by the random choice of sequence and index i”だねと、分ったのだった （なぜ、mathoverflow>>465 の手法が成立たないのか？ ”CONGLOMERABILITY”が成立ってないというのが、数学DR Alexander Pruss氏の指摘（2013）で、それを2018年の著書で詳しく解説している） スレ65 https://rio2016.5ch.net/test/read.cgi/math/1557142618/750-754 https://books.google.co.jp/books?id=RXBoDwAAQBAJ&pg=PA77&lpg=PA77&dq=%22conglomerability%22+assumption+math&source=bl&ots=8Ol1uFrjJQ&sig=ACfU3U1bAurNGJm5872wDblskzsSgsU0iA&hl=ja&sa=X&ved=2ahUKEwioiPyV_IPiAhXHxrwKHUeaArUQ6AEwCXoECEoQAQ#v=onepage&q=%22conglomerability%22%20assumption%20math&f=false Infinity, Causation, and Paradox 著者: Alexander R. Pruss Oxford University Press, 2018 P75 (抜粋) 2.5.3 COUNTABLE ADDITITVITY AND CONGLOMERABILITY (引用終り) http://rio2016.5ch.net/test/read.cgi/math/1565872684/301

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