作者asdfghjk (asdfghjk)
看板Math
标题Re: [分析] 初微(18)
时间Sat Jul 16 21:30:42 2005
※ 引述《PttFund (批踢踢基金)》之铭言：
: Suppose that f in R([a,b]). Show that f^2 in R([a,b]).
: Notation: R([a,b]) is the set of all Riemann integrable
: functions on [a,b].
Since f belongs to R([a,b])
f is bounded, i.e. |f| < M for some M > 0
and for any ε > 0
there is a partition Π on [a,b] such that
U(f;Π) - L(f;Π) < ε/2M
consider U(f^2;Π) - L(f^2;Π) < 2M [U(f;Π) - L(f^2;Π)] < ε
by Darboux's Criterion
f^2 belongs to R([a,b])
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