Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

The equivalence of some Bernoulli convolutions to Lebesgue measure
HTML articles powered by AMS MathViewer

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
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 26A30, 28A78, 28A80
  • Retrieve articles in all journals with MSC (1991): 26A30, 28A78, 28A80
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