Some remarks on the property (N) of Luzin


We consider the classical property (N) of Luzin for various mappings in connection with a measure extension problem. We give some examples of Borel measurable mappings and of Lebesgue measurable mappings which transform all compact sets with measure zero into sets with measure zero but do not have the property (N) of Luzin.

1. N. Luzin, Integral and Trigonometric series, Moscow, 1956 (in Russian).
2. M. Ershov, Measure Extensions and Stochastic Equations, Probability Theory and its Applications, 19 (3), 1974 (in Russian).
3. C. Dellacherie, Capacities et Processus Stochastiques, Springer-Verlag, Berlin, 1972.
4. A. Kharazishvili, Some questions of set theory and measure theory, Tbil. Gos. Univ., Tbilisi, 1978 (in Russian).
5. Handbook of Mathematical Logic, (Ed. J. Barwise), North-Holland Publ. Comp., Amsterdam, 1977.

Published : 1995-09-29

KharazishviliA. B. (1995). Some remarks on the property (N) of Luzin. Annales Mathematicae Silesianae, 9, 33-41. Retrieved from

Alexander B. Kharazishvili 
Institute of Applied Mathematics, Tbilisi State University, Georgia  Georgia

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