Prove that ∫(1,∞) 1/x dx=∞(as a Lebesgue integral).证明 ∫(1,∞) 1/x dx=∞ (勒贝格积分)

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Prove that ∫(1,∞) 1/x dx=∞(as a Lebesgue integral).证明 ∫(1,∞) 1/x dx=∞ (勒贝格积分)
Prove that ∫(1,∞) 1/x dx=∞
(as a Lebesgue integral).
证明 ∫(1,∞) 1/x dx=∞ (勒贝格积分)

Prove that ∫(1,∞) 1/x dx=∞(as a Lebesgue integral).证明 ∫(1,∞) 1/x dx=∞ (勒贝格积分)
考虑这样一个数列an=(R)∫(1,n) 1/x dx=ln(n),
由于这是一个在闭区间上R可积的积分,所以必然L可积且积分相等,在任意m>0,存在N当n>N时有an>M.简单思路就是这样,具体的东西还得你自己去看.

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