臺灣博碩士論文加值系統

　 此篇文章中，我們主要是探討定義於R^n上之所謂〝Uniformly Distributed Measure〞。
　　在1987年，Preiss教授所發表的文章中，將關於此類測度的幾何性質做了些許之探究；其內容主要是藉由測度所衍生出之moments,以其對s之漸近行為，而獲致有關測度之support的巨觀表象。
　　我們將試著更進一步地了解與探究moments所扮演的角色及其重要性
；另外，我們也以另一角度與方法，獲致類似的結果，並與[P]中之証明推論作一比較。

In this essay, we consider the so called uniformly
distributed measure over R^n. In [P], geometric properties for
such measures had been derived. Practically, all the main
results and conclusions in [P] are all based upon behavior of
approximation of momentsof the measure Φ by polynomial in s to certain order when s → ∞ and when s↘0.
To investigate the support of a measure, we usually look at its tangent measures so that a global view for its support
can be obtain. For this purpose, we try to look more closely
these moments, and, for comparison,to give other approaches to obtain some of results in [P].

1.Introduction.................................................2
2.Preliminaries................................................3
3.Moments of Measures over R^n................................11
4.Supports for Uniformly Distributed Measures over R^n........15
5.Some Remarks of Uniformly Distributed Measure over R^n......27

[P] D.Preiss, Geometry of Measures in R^n :Distribution,
rectifiability, and densities, Ann. of Math.125 (1987),
537-643.
[M] P. Mattila, Geometry of Sets and Measures in Euclidean
Spaces: Fractals and rectifiability, Cambridge University
Press, 1995.
[F] H. Federer, Geometric Measure Theory, Springer-Verlag,
New York, 1969.
[Fa] K. J. Falconer, Geometry of Fractal Sets, Cambridge
University Press, 1985.