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On the convergence of Σ∞n = 1f(nx) for measurable functions

Part of: Classical measure theory

Published online by Cambridge University Press:  26 February 2010

Zoltán Buczolich  and
R. Daniel Mauldin
Zoltán Buczolich
Affiliation:
Department of Analysis, Eőtvős Loránd University, Budapest, Hungary. E-mail: buczo@ludens.elte.hu
R. Daniel Mauldin
Affiliation:
Department of Mathematics, University of North Texas, Denton, Texas 76203, U.S.A. E-mail: mauldin@unt.edu
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Abstract

Questions of Haight and of Weizsäcker are answered in the following result. There exists a measurable function f: (0, + ∞) → {0,1} and two non-empty intervals IFI∞⊂[½,1) such that Σ∞n = 1f(nx) = +∞ for everyx εI∞, and Σ∞n = 1f(nx) >+∞ for almost every xεIf. The function f may be taken to be the characteristic function of an open set E.

MSC classification

Secondary: 28A35: Measures and integrals in product spaces
Type
Research Article
Information
Mathematika , Volume 46 , Issue 2 , December 1999 , pp. 337 - 341
Copyright
Copyright © University College London 1999

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References

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