查看“︁黎曼测度”︁的源代码

'''黎曼测度'''可指：

*[[黎曼度量]]（{{lang-en|Riemannian metric}}），描述黎曼流形上距離、體積、角度等結構的張量。<ref>{{cite journal|title = 关于两个黎曼测度的芬斯拉乘积空间|author = 苏步青|url = https://www.cnki.com.cn/Article/CJFDTotal-FDXB195902000.htm|quote = 黎曼测度张量|journal = |access-date = 2022-03-14|archive-date = 2022-02-12|archive-url = https://web.archive.org/web/20220212033223/https://www.cnki.com.cn/Article/CJFDTotal-FDXB195902000.htm|dead-url = no}}</ref><ref>{{cite journal|title = 常曲率空間中超曲面的變形与平均曲率|author = 胡和生|url = https://www.cnki.com.cn/Article/CJFDTotal-FDXB195601012.htm|quote = 任何曲面V<sub>2</sub>有二維的黎曼测度ds<sup>2</sup>=Edu<sup>2</sup>+2 Fdudv+Gdv<sup>2</sup>,這就是曲面V<sub>2</sub>的第一基本形式|journal = |access-date = 2022-03-14|archive-date = 2020-11-26|archive-url = https://web.archive.org/web/20201126233717/http://www.cnki.com.cn/Article/CJFDTOTAL-FDXB195601012.htm|dead-url = no}}</ref>
*黎曼流形的[[測度]]（{{lang-en|Riemannian measure}}），依照黎曼度量導出的測度，用於計算體積及函數的積分。<ref>{{cite web|author = 王作勤|title = The Riemannian Measure|series = 黎曼几何（英）（2016 春季学期）| url = http://staff.ustc.edu.cn/~wangzuoq/Courses/16S-RiemGeom/Notes/Lec03.pdf}}</ref><ref>{{cite web|author = F.E. Burstall|url = https://people.bath.ac.uk/feb/papers/icms/paper.pdf|title = Basic Riemannian Geometry|page = 11|access-date = 2022-03-14|archive-date = 2021-06-20|archive-url = https://web.archive.org/web/20210620033658/https://people.bath.ac.uk/feb/papers/icms/paper.pdf|dead-url = no}}</ref><ref>{{cite web|author = ftliang| url = https://idv.sinica.edu.tw/ftliang/diff_geom/*diff_geometry(II)/3.25/volume_comparison/3Riemann_measure.pdf |title = Riemannian measure |website = idv.sinica.edu.tw}}</ref><ref>{{cite book|author = Takashi Sakai|chapter = 5 Riemannian Measure| url = https://www.google.co.uk/books/edition/Riemannian_Geometry/aqgaZVr94xMC?hl=en&gbpv=1&dq=riemannian+measure&pg=PA61&printsec=frontcover|title = Riemannian Geometry|year = 1996|publisher = American Mathematical Society}}</ref>與前者的關係見{{le|Metric tensor#Canonical measure and volume form}}。
*定義實數集<math>\mathbb R</math>某類子集大小的一種方法：考慮<math>\mathbb R</math>上的區間（包括无穷区间），關於有限併及有限差封閉而成的环<math>R</math>（它不是<math>\sigma</math>环）。對於<math>A \in R</math>，定义<math>\mu(A)</math>為组成<math>A</math>的各区间的长度之和，则<math>\mu</math>稱為<math>R</math>上的黎曼测度。<ref>{{cite book|title = 应用泛函分析|author1 = 门少平|author2 = 封建湖|url = http://www.ecsponline.com/yz/B3B53C07F9E004AC49074DB2DB7FB0E27000.pdf|publisher = 科學出版社|location = 北京|year = 2005|page = 10}}</ref>

== 參考文獻 ==
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[[Category:测度论]]