On measurable Sierpiński-Zygmund functions

• Autorzy: Kharazishvili A. B.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Sierpiński-Zygmunt functions; absolutely nonmeasurable function; universal measure zero set; extension of measure; thick graph; invariant measure

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2006
• Tom: Vol. 12, nr 2
• Strony: 283--292
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Kharazishvili A. B.

• I. Vekua Institute of Applied Mathematics of Tbilisi State University University Street 2 Tbilisi 0143, Georgia and A. Razmadze Institute of Mathematics of Georgian Academy of Sciences M. Alexidze Street 1 Tbilisi 0194, Georgia,

Bibliografia

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• [2] Kharazishvili, A. B., Invariant measures in Hilbert space (in Russian), Soobshch. Akad. Nauk Gruzin. SSR 114(1) 1984, 41-44.
• [3] Kharazishvili, A. B., Tansformation Groups and Invariant Masures. Set-Theoretical Aspects. World Scientific Publishing Co., Inc., River Edge, NJ, 1998.
• [4] Kharazishvili, A. B., Stronge Punctions in Real Analysis, Pure and Appl. Math. (N.Y.) 229, Marcel Dek ker, Inc., New York, 2000.
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• [8] Miller, A. W., Special subsets of the real line, in "Handbook of Set-Theoretic Topology", North-Holland, Amsterdam, 1984.
• [9] Natkaniec, T., Rosen, H., An example of an additive almost continuous Sierpiński-Zygmund function, Real Anal. Exchange 30(1) (2004-2005), 261-266.
• [10] J.C. Oxtoby, Measure and Category, Springer-Verlag, Berlin, 1971.
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