[分析] 黎曼積分的一個等價敘述
f:[a,b]→R bounded
由高微書給的黎曼可積分定義
For each ε>0, there exists a partition P such that U(f,P)-L(f,P)<ε
怎麼證出, 他會等價於
For each ε>0, there exists δ>0, such that
for all partition P with |P|<δ and all sample set T(在分割內任意取點的集合)
such that |S(f,P,T)-∫f dx|<ε
其中 S(f,P,T)是參照分割P跟抽樣集T的黎曼和, ∫f dx是黎曼積分.
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不叫 Darboux 定理, Darboux 定理是講別的.
看起來好證, 但不太好證耶.
※ 編輯: alfadick (36.227.241.1), 09/03/2016 00:09:29
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