Orthogonal decomposition of the Gaussian measure

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• 作者：S. G. Haliullin
• 刊名：Lobachevskii Journal of Mathematics
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：37
• 期：4
• 页码：436-438
• 全文大小：474 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Algebra
  Analysis
  Geometry
  Mathematical Logic and Foundations
  Probability Theory and Stochastic Processes
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1818-9962
• 卷排序：37

文摘

The ultrapower of real line, R_U, where U is a nontrivial ultrafilter in the set the N of natural integers, is some realizations of the “non-standard expansion” *R of the set of real numbers. Due to “good” properties of the factorization of cartesian productwith respect to ultrafilter, ultraproducts hold a number of considerable value properties from the algebraic point of view. At the same time it is not any good “natural” (i.e. determined by the topology of factors) topology. In this article some properties of the Gaussian measure defined on ultraproduct of linear measurable spaces are investigated. In particular, we will give an example of a Gaussian not extreme measure. It will be defined on the linear measurable space which doesn’t have any topological structure. For the proof of many statements of the work the technics of the ultraproducts developed in work [1] is used.Keywords and phrasesLinear measurable spaceUltraproductsGaussian measure