※ 引述《chopriabin ()》之銘言：
: Suppose that
: 1. f(x) is a continuous nonnegative function for x in R with the property
: that f(x) is non-increasing in x and \int_{0}^{\infty} f(x) dx<\infinity.
non-increasing 這裡應該滿重要的，你可以由這一點和 f≧0 屬於 L^1導出
lim f(x) = 0。不然你的結論可能不成立...
x→∞
: 2. {x_n} is a nonnegative sequence with x_n converging to x_0 when n tends
: to infinity. Must f(x_n) approach to f(x_0) as x_n tends to infinity ?
: Prove or disprove.
所以是要證明 lim f(x_n) = lim f(x) for every real sequence {x_n} with
n→∞ x→∞
limit = +∞ 的意思？
那這樣是有的，從 lim f(x) = 0 就可看出
x→∞
有錯請指教
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