[分析] Royden的習題

[wyob (Go Dolphins)]

For each of the two functions f on [1,∞) defind below,show that      n
                                                                lim  ∫f
                                                                n→∞ 1
exists while f is not integrable over [1,∞).Does this constradict the

continuity of integrable?

(i) Define f(x)=[(-1)^n]/n,for n≦x＜n+1.

(ii)Define f(x)=(sinx)/x for1≦x＜∞.

看不太懂題目，有高手可以解惑一下嗎

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※ 編輯: wyob            來自: 134.208.85.174       (01/02 23:30)
推 herstein    :意思就是說叫你證明極限存在雖然函數並不是可積