“Darboux's theorem”的概念、定义、习题解题方法及翻译-数学辞典

单词

Darboux's theorem

释义

Darboux's theorem

(Darboux integral) Darboux's integral is an alternative theory of integration which is equivalent to Riemann's. Let f(x) be a bounded real-valued function on the interval [a,b]. Then both of the following are well defined

These are respectively referred to as the lower and upper Riemann or Darboux integrals of f. Then f is said to be Darboux integrable if the lower and upper integrals are equal, and this is equivalent to being Riemann integrable. The Dirichlet function on [a,b] has lower integral 0 and upper integral b–a and so is not Darboux or Riemann integrable.

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