The equivalence of some Bernoulli convolutions to Lebesgue measure
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- by R. Daniel Mauldin and Károly Simon PDF
- Proc. Amer. Math. Soc. 126 (1998), 2733-2736 Request permission
Abstract:
Since the 1930’s many authors have studied the distribution $\nu _{\lambda }$ of the random series $Y_{\lambda }=\sum \pm {\lambda }^n$ where the signs are chosen independently with probability $(1/2,1/2)$ and $0<\lambda <1$. Solomyak recently proved that for almost every $\lambda \in [\frac {1}{2},1],$ the distribution $\nu _{\lambda }$ is absolutely continuous with respect to Lebesgue measure. In this paper we prove that $\nu _{\lambda }$ is even equivalent to Lebesgue measure for almost all $\lambda \in [\frac {1}{2},1]$.References
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Additional Information
- R. Daniel Mauldin
- Affiliation: Department of Mathematics, P. O. Box 305118, University of North Texas, Denton, Texas 76203-5118
- Email: mauldin@dynamics.math.unt.edu
- Károly Simon
- Affiliation: Department of Mathematics, P. O. Box 305118, University of North Texas, Denton, Texas 76203-5118
- Address at time of publication: Institute of Mathematics, University of Miskolc, Miskolc-Egyetem- varos, H-3515 Hungary
- MR Author ID: 250279
- Email: matsimon@gold.uni-miskolc.hu
- Received by editor(s): February 11, 1997
- Additional Notes: The first author’s research was supported by NSF Grant DMS-9502952. The second author’s research was partially supported by grants F19099 and T19104 from the OTKA Foundation
- Communicated by: Frederick W. Gehring
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 2733-2736
- MSC (1991): Primary 26A30, 28A78, 28A80
- DOI: https://doi.org/10.1090/S0002-9939-98-04460-8
- MathSciNet review: 1458276