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On Measurable Sierpiński-Zygmund Functions
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A. B. Kharazishvili
Published/Copyright:
June 9, 2010
Abstract
It is proved that there exists a Sierpiński-Zygmund function, which is measurable with respect to a certain invariant extension of the Lebesgue measure on the real line ℝ.
Key words and phrases.: Sierpiński-Zygmund function; absolutely nonmeasurable function; universal measure zero set; extension of measure; thick graph; invariant measure
Received: 2005-09-19
Revised: 2006-01-27
Published Online: 2010-06-09
Published in Print: 2006-December
© Heldermann Verlag
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Keywords for this article
Sierpiński-Zygmund function;
absolutely nonmeasurable function;
universal measure zero set;
extension of measure;
thick graph;
invariant measure
Articles in the same Issue
- and Ultrafilters on ℚ and ω
- Remarks on Best Approximations in Generalized Convex Spaces
- A Note on P-Times and Time Projections
- The Apollonian Metric: The Comparison Property, Bilipschitz Mappings and Thick Sets
- On the Integral Quasicontinuity
- On Completeness of Random Transition Count for Markov Chains
- Notes on Uniqueness of Meromorphic Functions
- Strong and Weak Convergence of Implicit Iterative Process with Errors for Asymptotically Nonexpansive Mappings
- On Measurable Sierpiński-Zygmund Functions
- Extension Theorem for a Functional Equation
