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Bernoulli Maps of a Lebesgue Space

Published online by Cambridge University Press:  20 November 2018

Imohimi C. Alufohai
Imohimi C. Alufohai*
Affiliation:
Department of mathematics, University of Benin, Benin City, Nigeria, West Africa
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Abstract

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A collection of measure preserving mappings having Bernoulli generators is considered. Only three conditions are required to be satisfied, and they are quite easy to check.

Keywords

28D0558F13
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 31 , Issue 1 , 01 March 1988 , pp. 26 - 31
Copyright
Copyright © Canadian Mathematical Society 1988

References

1. Adler, R. L., F-expansions revisited, Springer lecture notes 318 (1973), pp. 1–5.Google Scholar
2. Adler, R. L., Continued fractions and Bernoulli Trials, in: Ergodic Theory. Moser, J., Phillips, E., Varadhan, S. (eds.). Lecture notes, New York: Courant Inst. Math. Sci. (1975).Google Scholar
3. Alufohai, I. C., A note on the ergodic theory of a class of number theoretical endomorphisms with o-finite invariant measure, Proceedings, 2nd International Symposium in West Africa on Functional Analysis and its applications, (1979), pp. 272–281.Google Scholar
4. Alufohai, I. C., A class of weak Bernoulli transformations associated with representations of real numbers, J. London Math. Soc. 2 (1981), pp. 295–302.Google Scholar
5. Alufohai, I. C., Number theoretical weak Bernoulli transformations on the unit interval, Math. Japoniea 29, 2 (1984), pp. 229–235.Google Scholar
6. Alufohai, I. C., Markov maps on a Lebesgue Space, (Submitted).Google Scholar
7. Bowen, R., Bernoulli maps of the interval, Israel J. Math. 28 (1977), pp. 161–168.Google Scholar
8. Bowen, R., Invariant measures for Markov maps of the interval, Commun. Math. Phys. 69 (1979), pp. 1–17.Google Scholar
9. Feldman, J., New K-automorphisms and a problem of Kakutani, Israel J. Math. 24 (1976), pp. 16–37.Google Scholar
10. Fischer, R., Ergodische Théorie von Ziffernentwicklungen in Wahrscheintichkeitsraumen, Math. Z. 128(1972), pp. 217–230.Google Scholar
11. Ratner, M., Bernoulli flows over maps of the interval, Israel J. Math. 31 (1978), pp. 298–314.Google Scholar
12. Schweiger, F., Numbertheoretical endomorphisms with o-finite invariant measure, Israel J. Math. 21 (1975), pp. 308–318.Google Scholar
13. Schweiger, F., Uber einen Algorithmum Von R. Gùting, J. reine angew. Math. 293/294 (1977), pp. 263–270.Google Scholar
14. Waterman, M. S., Kuzmin theorem for a class of number theoretic endomorphisms, Acta Arith. 19(1971), pp. 31–41.Google Scholar
15. Williams, R. F., The structure of Lorenz attractors, IHES Pub. 50 (1979), pp. 321–347.Google Scholar