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度规的意义

The meaning of DuGui

王小舟

本文以数轴为工具定义了度规和度规积分的概念,同时证明了在一定条件下度规积分与黎曼积分等价。度规积分从另一个角度揭示了微积分的基本性质。最后指出度规是基于度量的概念,度量离不开度规的存在。

数学

度规度规积分度规导数变度规实数轴度规度量

王小舟.度规的意义[EB/OL].(2006-09-04)[2025-09-26].http://www.paper.edu.cn/releasepaper/content/200609-27.点此复制

This paper presents the conception of DuGui and the integration of DuGui, which are defined by the using of number axis as a tool. The equivalence between the integration of DuGui and the integration of Riemann at a certain condition is also proved in this paper. The integration of DuGui open out the basic character of calculous from another point of view. At last, it points out that the conception of DuGui is based on the measurement conception, while the conception of Measurement can not exist without the conception of DuGui.

Keywords: DuGui Integration of DuGui Derivative of DuGui Real Number Axis with Variational DuGui Mesurement of DuGui

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