b****t
发帖数: 114 | 1 Hi all,
I am in Engineering, so please bear with me for possibly native questions...
A sequence of functions f_n converges to f on (a,b) in R, and if f'n
uniformly converges on (a,b), then f'n converges to f'. This result can be
seen from many testbook (.e.g Rudin's analysis book). But does this result
hold for f_n and f on a set of R^n, with the same assumptions?
Thank you very much.
Beet | l****y
发帖数: 4773 | | b****t
发帖数: 114 | 3 为啥要答非所问呢？
【在 l****y 的大作中提到】
: 一致收敛比收敛强
| B********e
发帖数: 10014 | 4 如果你所有的convergence都是指uniform convergence，fn ，fn'，f都连续可微，那
么yes。
因为任何一闭区间上都yes。
设fn'一致收敛于g。
在任一有界区间上，写出积分关系，取极限。 |
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