推 math1209 :-) 11/25 19:03
推 smarter1004 :XDDD 好樣的 感謝您的解答 但如果我改問V是否一定 11/25 20:37
→ smarter1004 :非閉集呢? 謝謝囉 11/25 20:37
※ 引述《smarter1004 (學海無涯)》之銘言：
: V為R^2中一子集且V在x軸的投影為[0,1]
: 收集
: F = {f:[0,1] → R ; (x,f(x)) is in V for all x in [0,1]}
: 若F中沒有一個函數是可測的
: 那麼是否V就是不可測的呢?
: 謝謝!
No. Counterexample:
Let S be a nonmeasurable subset of [0, 1], and consider
V = S×{1} ∪ ([0,1]\S)×{0}.
Then F only contains the indicator function on S,
which is not measurable, but V is a subset of the null set
[0, 1]×{0, 1}
and hence is Lebesgue measurable (because of completion). □
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※ 編輯: cgkm 來自: 75.62.141.216 (11/25 16:12)