Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-29T06:55:17.706Z Has data issue: false hasContentIssue false

Finite Dimensional Approximations to Some Flows on the Projective Limit Space of Spheres II

Published online by Cambridge University Press:  22 January 2016

Hisao Nomoto*
Affiliation:
Nagoya University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In the previous paper [6], we have considered flows on the measure space (Ω, ℬ, P), which was the projective limit of a certain subspace (Ωn, ℬn, Pn) of the measure space (Sn, (Sn), Pn), where Sn is the (n − 1) · sphere with radius and Pn is the uniform probability distribution over Sn.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1967

References

[1] Bochner, S., Harmonic Analysis and the Theory of Probability, Uni. of Calf. Press, 1955.Google Scholar
[2] Hida, T., Finite dimensional approximations to White noise and Brownian motion., J. Math. Mech., (to appear).Google Scholar
[3] Hida, T. and Nomoto, H., Gaussian Measure on the Projective Limit Space of Spheres., Proc. Japan Acad., 40 (1964), 301304.Google Scholar
[4] Hopf, Eberhard, Ergodentheorie, Erg. Math. 5, No. 2, 1937.Google Scholar
[5] Lévy, P., Problems concrets d’analyse fonttionelle, Gauthier-Villars, 1951.Google Scholar
[6] Nomoto, H., Finite dimensional approximations to some flows on the projective limit space of spheres., (to appear).Google Scholar
[7] Rohlin, V. A., On the fundamental ideas of measure theory, Amer. Math. Soc. Translations Ser. 1, 10 (1961), 154.Google Scholar
[8] Rota, G.-C., On the classification of periodic flows., Proc. Amer. Math. Soc, 13 (1962) 659662.Google Scholar
[9] Totoki, H., Flows and Entropy. Seminar on Prob., 20 (1964), 1130 (Japanese).Google Scholar