Remarks on Type 0 Cylindrical Measures

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概要

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• For a probability measure μ defined on a finite dimensional space R^n, we have another measure as follows: λ(=∫_<u∈O(n)>μ(u()dm_n(u), where O(n) is the family of all unitary operators on R^n and m_n is the normalized Haar measure defined on O(n). Thus we can make a rotationally invariant measure λ from μ. λ is an average of μ with respect to rotations. Can we have the same result about cylindrical measures on an infinite dimensional space? The answer is "yes" for special kinds of cylindrical measures, for example, (strongly) rotationally quasi-invariant ((S)RQI) cylindrical measures (in fact, these coincide with RQI-cylindrical measures [5]). In the former half part of this paper, we treat the above problem for type 0-cylindrical measures. We present the main result in chapter 1. The latter half part gives a detailed account of the relation between Shimomura's result ([5]) and GRQI-cylindrical measures ([2]) concerning the case of type 0-cylindrical measures.

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著者

• Maeda Michie

  Department Of Mathematics Faculty Of Science Ochanomizu University

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