f is complex-valued function defined in R^1 and f is conti. at t=0
經過一些運算可以得到下列不等式
|f(t)-f(t+h)|^2 =< 4|1-f(h)| (過程略過)
Thus the "modulus of continuity" at each t is bounded by twice
the square root of that at 0; and so continuity at 0 implies
uniform continuity everywhere.
先說明我的看法, 當 h 趨近 0, |f(t)-f(t+h)|^2趨近於 0, 跟 t 無關
故f 是 uniform continuous everywhere
但就書中的解釋似乎不是那麼容易就可以得到此結論, 是少了哪個部份呢??
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※ 編輯: quetion 來自: 140.127.226.30 (09/02 16:29)