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On Superrecurrence

Published online by Cambridge University Press:  20 November 2018

Karma Dajani
Karma Dajani*
Affiliation:
George Washington University, Department of Mathematics, Washington D.C. 20052, USA
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Abstract

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Let T be a non-singular, conservative, ergodic automorphism of a Lebesgue space. We study a kind of weighted cocycles called H-cocycles. We introduce the notions of H-superrecurrence and H-supertransience. We use skew products to give necessary and sufficient conditions for H-superrecurrence.

Keywords

28D9947A3560J1534C35.
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 1 , 01 March 1991 , pp. 48 - 57
Copyright
Copyright © Canadian Mathematical Society 1991

References

1. Atkinson, G., Recurrence ofcocycles and random walks, J. London Math. Soc. 13(2)(1976), 486-488. 2. Chung, K. L. and Fuchs, W., On the distribution of values of sums of random variables, Mem. Amer. Math. Soc. 6 (1951), 1–12.Google Scholar
3. Schmidt, K., Cocycles ofergodic transformation groups. MacMillen Lectures in Mathematics. New Delhi, MacMillen, India, 1977.Google Scholar
4. Schmidt, K., On recurrence, Z. Wahrscheinlichkeitstheorie verw. Geb. 68 (1984), 75–95.Google Scholar
5. Ullman, D., A generalization of a theorem of Atkinson to non-invariant measures, Pacific J.of Math. 130(1)(1987).Google Scholar
6. Ullman, D., Ph.D. dissertation, Berkeley.Google Scholar