The study of the topological support of a Gaussian measure in a Banach space
碩士 === 國立高雄大學 === 應用數學系碩士班 === 100 === In [4] , K . Itô showed that for a given Gaussian measure on a real separable Hilbert space , it’s topological support coincides with the least closed subspace with the total measure. The purpose of this study will be devoted to extend Itô’s result to a Gaussia...
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| Format: | Others |
| Language: | en_US |
| Published: |
2012
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| Online Access: | http://ndltd.ncl.edu.tw/handle/13010135023193509420 |
| Summary: | 碩士 === 國立高雄大學 === 應用數學系碩士班 === 100 === In [4] , K . Itô showed that for a given Gaussian measure on a real separable Hilbert space , it’s topological support coincides with the least closed subspace with the total measure. The purpose of this study will be devoted to extend Itô’s result to a Gaussian measure on a real separable Banach space. As a simple application , for any real separable Banach space B on which a Gaussian measure with zero mean is given , a method to construct a standard countably Hilbert space setting from will be presented .
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