Optimal estimation of shell thickness in Cutland's construction of Wiener measure
文献类型：期刊论文
| 作者 | Li, BH; Li, YQ |
| 刊名 | PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
 |
| 出版日期 | 1998 |
| 卷号 | 126期号:1页码:225-229 |
| 关键词 | shell thickness Wiener measure *-finite Euclidean space |
| ISSN号 | 0002-9939 |
| 英文摘要 | 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). |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000071753600030 |
| 出版者 | AMER MATHEMATICAL SOC |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/13580]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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