Projective Limit of Haar Measures on $O(n)$ | Zendy

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Projective Limit of Haar Measures on $O(n)$

Author(s) -

Yasuo Yamasaki

Publication year - 1972

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.786

H-Index - 39

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.2977/prims/1195193230

Subject(s) - mathematics , limit (mathematics) , pure mathematics , haar , projective test , inverse limit , combinatorics , mathematical analysis , computer science , artificial intelligence , wavelet

In this paper, we shall show that the Gaussian measure £l~] on R is obtained as the projective limit of Haar measures on 0(n\ This is a natural extension of the fact [J2] Q3] : the Gaussian measure on R°° is obtained as the projective limit of the uniform measures on the ndimensional spheres. D. Shale ^4] considered the family of Haar measures on 0(n) to construct a finitely additive measure on 0(oo). But he did not treat the projective limit. Also a report by H. Shimomura £5] is useful for the information on this topic.

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