Optimal estimation of shell thickness in Cutland's construction of Wiener measure

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	Optimal estimation of shell thickness in Cutland's construction of Wiener measure
	Li, BH; Li, YQ
	1998
发表期刊	PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN	0002-9939
卷号	126 期号:1 页码:225-229
摘要	In Cutland's construction of Wiener measure, he used the product of Gaussian measures on R-N, where N is an infinite integer. It is mentioned by Cutland and Ng that for the product measure gamma, gamma({x : R-1 less than or equal to \\x\\ less than or equal to R-2}) similar or equal to 1, where R-1 = 1 - (logN)N-1/2(-1/2) and R-2 = 1 + MN-1/2 with M any positive infinite number. We prove here that R-1 may be replaced by 1 - mN(-1/2) with m any positive infinite number. This is the optimal estimation for the shell thickness. It is also proved that gamma({x : \\x\\ < 1}) similar or equal to gamma({x : \\x\\ > 1}) similar or equal to 1/2. And for the Lebesgue measure mu, mu({x : \\2\\ less than or equal to r}) is finite and not infinitesimal iff r = (2 pi e)(-1/2)N(1/2(1+1/N)e(a/N) with a finite, while for the *Lebesgue area of the sphere SN-1(r), r should be (2 pi e)(-1/2)N(1/2)e(a/N).
关键词	shell thickness Wiener measure *-finite Euclidean space
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000071753600030
出版者	AMER MATHEMATICAL SOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/13581
专题	中国科学院数学与系统科学研究院
通讯作者	Li, BH
作者单位	Acad Sinica, Inst Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Li, BH,Li, YQ. Optimal estimation of shell thickness in Cutland's construction of Wiener measure[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY,1998,126(1):225-229.
APA	Li, BH,&Li, YQ.(1998).Optimal estimation of shell thickness in Cutland's construction of Wiener measure.PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY,126(1),225-229.
MLA	Li, BH,et al."Optimal estimation of shell thickness in Cutland's construction of Wiener measure".PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 126.1(1998):225-229.