Equipartition of interval partitions and an application to number theory
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- by Karma Dajani and Adam Fieldsteel PDF
- Proc. Amer. Math. Soc. 129 (2001), 3453-3460 Request permission
Abstract:
We give wider application and simpler proofs of results describing the rate at which the digits of one number-theoretic expansion determine those of another. The proofs are based on general measure-theoretic covering arguments and not on the dynamics of specific maps.References
- Jose Barrionuevo, Robert M. Burton, Karma Dajani, and Cor Kraaikamp, Ergodic properties of generalized Lüroth series, Acta Arith. 74 (1996), no. 4, 311–327. MR 1378226, DOI 10.4064/aa-74-4-311-327
- Bosma, W., K. Dajani and C. Kraaikamp - Entropy and counting correct digits, University of Nijmegen, report no. 9925, 1999. http://www-math.sci.kun.nl /math/onderzoek/reports/reports1999.html
- Patrick Billingsley, Ergodic theory and information, John Wiley & Sons, Inc., New York-London-Sydney, 1965. MR 0192027
- Gustav Lochs, Vergleich der Genauigkeit von Dezimalbruch und Kettenbruch, Abh. Math. Sem. Univ. Hamburg 27 (1964), 142–144 (German). MR 162753, DOI 10.1007/BF02993063
- A. Rényi, Representations for real numbers and their ergodic properties, Acta Math. Acad. Sci. Hungar. 8 (1957), 477–493. MR 97374, DOI 10.1007/BF02020331
- Fritz Schweiger, Ergodic theory of fibred systems and metric number theory, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1995. MR 1419320
Additional Information
- Karma Dajani
- Affiliation: Department of Mathematics, Utrecht University, 3508TA Utrecht, The Netherlands
- Email: dajani@math.uu.nl
- Adam Fieldsteel
- Affiliation: Department of Mathematics, Wesleyan University, Middletown, Connecticut 06459
- Email: afieldsteel@wesleyan.edu
- Received by editor(s): March 8, 2000
- Published electronically: June 27, 2001
- Additional Notes: The first author was partially supported by NWO grant no. 61-449
We wish to thank Ethan Coven for useful observations. - Communicated by: Michael Handel
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 3453-3460
- MSC (1991): Primary 11Kxx, 28Dxx
- DOI: https://doi.org/10.1090/S0002-9939-01-06299-2
- MathSciNet review: 1860476