A characterization of homeomorphic Bernoulli trial measures
HTML articles powered by AMS MathViewer
- by Andrew Q. Yingst PDF
- Trans. Amer. Math. Soc. 360 (2008), 1103-1131 Request permission
Abstract:
We give conditions which, given two Bernoulli trial measures, determine whether there exists a homeomorphism of Cantor space which sends one measure to the other, answering a question of Oxtoby. We then provide examples, relating these results to the notions of good and refinable measures on Cantor space.References
- Ethan Akin, Good measures on Cantor space, Trans. Amer. Math. Soc. 357 (2005), no. 7, 2681–2722. MR 2139523, DOI 10.1090/S0002-9947-04-03524-X
- Steve Alpern and V. S. Prasad, Typical dynamics of volume preserving homeomorphisms, Cambridge Tracts in Mathematics, vol. 139, Cambridge University Press, Cambridge, 2000. MR 1826331
- Tim D. Austin, A pair of non-homeomorphic product measures on the Cantor set, Math. Proc. Cambridge Philos. Soc. 142 (2007), no. 1, 103–110. MR 2296394, DOI 10.1017/S0305004106009741
- Eli Glasner and Benjamin Weiss, Weak orbit equivalence of Cantor minimal systems, Internat. J. Math. 6 (1995), no. 4, 559–579. MR 1339645, DOI 10.1142/S0129167X95000213
- K. Győry, Sur les polynômes à coefficients entiers et de discriminant donné, Acta Arith. 23 (1973), 419–426. MR 437489, DOI 10.4064/aa-23-4-419-426
- K. Győry, Sur les polynômes à coefficients entiers et de discriminant donné, Acta Arith. 23 (1973), 419–426. MR 437489, DOI 10.4064/aa-23-4-419-426
- Felix Hausdorff, Summationsmethoden und Momentfolgen. I, Math. Z. 9 (1921), no. 1-2, 74–109 (German). MR 1544453, DOI 10.1007/BF01378337
- K. J. Huang, Algebraic numbers and topologically equivalent measures in the Cantor set, Proc. Amer. Math. Soc. 96 (1986), no. 4, 560–562. MR 826481, DOI 10.1090/S0002-9939-1986-0826481-X
- G. G. Lorentz, Bernstein polynomials, Mathematical Expositions, No. 8, University of Toronto Press, Toronto, 1953. MR 0057370
- R. Daniel Mauldin, Problems in topology arising from analysis, Open problems in topology, North-Holland, Amsterdam, 1990, pp. 617–629. MR 1078668
- Francisco J. Navarro-Bermúdez, Topologically equivalent measures in the Cantor space, Proc. Amer. Math. Soc. 77 (1979), no. 2, 229–236. MR 542090, DOI 10.1090/S0002-9939-1979-0542090-0
- Francisco J. Navarro-Bermúdez and John C. Oxtoby, Four topologically equivalent measures in the Cantor space, Proc. Amer. Math. Soc. 104 (1988), no. 3, 859–860. MR 939966, DOI 10.1090/S0002-9939-1988-0939966-4
- John C. Oxtoby, Homeomorphic measures in metric spaces, Proc. Amer. Math. Soc. 24 (1970), 419–423. MR 260961, DOI 10.1090/S0002-9939-1970-0260961-1
- John C. Oxtoby and Vidhu S. Prasad, Homeomorphic measures in the Hilbert cube, Pacific J. Math. 77 (1978), no. 2, 483–497. MR 510936, DOI 10.2140/pjm.1978.77.483
- J. C. Oxtoby and S. M. Ulam, Measure-preserving homeomorphisms and metrical transitivity, Ann. of Math. (2) 42 (1941), 874–920. MR 5803, DOI 10.2307/1968772
- R. G. E. Pinch, Binomial equivalence of algebraic integers, J. Indian Math. Soc. (N.S.) 58 (1992), no. 1-4, 33–37. MR 1207024
- G. Pólya and G. Szegö, Problems and Theorems in Analysis II, Springer, 1972.
- R. D. Mauldin, R. Dougherty and A. Yingst, On homeomorphic Bernoulli measures on the Cantor space, to appear in Trans. Amer. Math. Soc., 16 pages.
Additional Information
- Andrew Q. Yingst
- Affiliation: Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208
- Address at time of publication: Department of Mathematics, University of South Carolina, P.O. Box 889, Lancaster, South Carolina 29721
- Email: andy.yingst@gmail.com
- Received by editor(s): July 17, 2006
- Published electronically: September 25, 2007
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 360 (2008), 1103-1131
- MSC (2000): Primary 28D05; Secondary 37B05, 28C15
- DOI: https://doi.org/10.1090/S0002-9947-07-04431-5
- MathSciNet review: 2346485