19/08/20 19:36:01.21 7640BXpe.net
>>510
>確率論からthe Continuum Hypothesisの不成立を主張したんだ
誤り
確率論の他に、Symmetryに関する前提を使用している
で、要はThe Brown-Freiling double dart throwの
集合S = {(p, q)/p, q 、 [0, 1] and p < q}
が下記の理由により非可測だといっている
p6
"we can say something stronger:
the set S is not a measurable set, and consequently Pr(p < q) is not defined.
If it were, then the conditions for applying Fubini’s Theorem would be satisfied.
We could compute the measure of S by iterated integrals and
it would not matter whether we used horizontal or vertical cross-sections.
These two ways of computing the integral would give the same result.
We know that they do not:
The measure of each vertical cross-section is 0,
while the measure of each horizontal cross-section is 1.
Hence, S is not measurable."
フビニの定理、知ってるか？ｗ