Full metadata record
DC Field | Value | Language |
---|---|---|
dc.contributor.author | 黃印良 | en_US |
dc.contributor.author | Yihn-Liang Hwang | en_US |
dc.contributor.author | 王夏聲 | en_US |
dc.contributor.author | Shiah-Sen Wang | en_US |
dc.date.accessioned | 2014-12-12T02:24:01Z | - |
dc.date.available | 2014-12-12T02:24:01Z | - |
dc.date.issued | 1999 | en_US |
dc.identifier.uri | http://140.113.39.130/cdrfb3/record/nctu/#NT880507010 | en_US |
dc.identifier.uri | http://hdl.handle.net/11536/66164 | - |
dc.description.abstract | 這篇論文的重點是研究在R^n上的均勻分布測度以及其切測度的各種幾何性質, 並且儘可能地對這些性質給予仔細而嚴密的證明。這些性質可以用來證明下面的定理: 若 (\Phi) 為 R^n 上的非零測度, m 為小於或等於 n 的非負整數, 且滿足對於所有的 x\in\spt\Phi,和 r>0,皆有 \Phi(B(x,r))=\alpha(m)*r^m 。 如果 m=0,1,2,n,則 (\Phi) 必是支集在 R^n 中某 m 維子空間上的一個 m 維 Hausdorff 測度。 本文中大部份的結果,請參看 David Preiss 的"Geometry of Measures in R^n: Distribution, Rectifiability, and Densities" (Ann. of Math. 125(1987), 537-643.)。 | zh_TW |
dc.description.abstract | In this thesis we study the uniformly distributed measures in R^n . Some basic properties of these measures and their tangent cones are proved in details. We also give an application of these properties in the last section: Let $\Phi$ be a nonzero measure over $\brn$, and $m\le n$ be an integer so that $\Phi(B(x,r))=\alpha(m)*r^{m}$, for every $x\in\spt\Phi$ and every $r>0$. In case of $m=0,1,2,n$, there is an $m$ affine subspace $V$ of $\brn$ such that $\Phi=H^m| V$. Most of the results in this thesis may be found in David Preiss' paper ([P]). | en_US |
dc.language.iso | en_US | en_US |
dc.subject | 均勻分布測度 | zh_TW |
dc.subject | 切測度 | zh_TW |
dc.subject | uniformly distributed measure | en_US |
dc.subject | tangent measure | en_US |
dc.subject | global Besicovitch property | en_US |
dc.subject | tangent cone | en_US |
dc.subject | Housdorff measure | en_US |
dc.subject | d-cone | en_US |
dc.subject | flat | en_US |
dc.subject | symmetric k linear form | en_US |
dc.title | N維歐氏空間上的均勻分布測度及其切測度 | zh_TW |
dc.title | Uniformly Distributed Measures in R^n | en_US |
dc.type | Thesis | en_US |
dc.contributor.department | 應用數學系所 | zh_TW |
Appears in Collections: | Thesis |