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2005/2006 On additive absolutely nonmeasurable Sierpiński-Zygmund functions.
A. B. Kharazishvili, A. Razmadze
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Real Anal. Exchange 31(2): 553-560 (2005/2006).


Assuming Martin's Axiom, it is proved that there exists a Sierpiński-Zygmund function, which is additive (i.e., is a solution of the Cauchy functional equation) and is absolutely nonmeasurable with respect to the class of all nonzero $\sigma$-finite diffused measures on the real line ${\mathbb R}$.


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A. B. Kharazishvili. A. Razmadze. "On additive absolutely nonmeasurable Sierpiński-Zygmund functions.." Real Anal. Exchange 31 (2) 553 - 560, 2005/2006.


Published: 2005/2006
First available in Project Euclid: 10 July 2007

zbMATH: 1114.28001
MathSciNet: MR2265796

Primary: 28A05
Secondary: 28D05

Keywords: $SZ$-function , absolutely nonmeasurable function , additive function , extension of measure. , universal measure zero set

Rights: Copyright © 2005 Michigan State University Press

Vol.31 • No. 2 • 2005/2006
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