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.
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.
The Copyright Holders of the submitted text are the Author and the Journal. The Reader is granted the right to use the pdf documents under the provisions of the Creative Commons 4.0 International License: Attribution (CC BY). The user can copy and redistribute the material in any medium or format and remix, transform, and build upon the material for any purpose.
This journal provides immediate open access to its content under the Creative Commons BY 4.0 license (http://creativecommons.org/licenses/by/4.0/). Authors who publish with this journal retain all copyrights and agree to the terms of the above-mentioned CC BY 4.0 license.
- Author’s Warranties
The author warrants that the article is original, written by stated author/s, has not been published before, contains no unlawful statements, does not infringe the rights of others, is subject to copyright that is vested exclusively in the author and free of any third party rights, and that any necessary written permissions to quote from other sources have been obtained by the author/s.
- User Rights
Under the Creative Commons Attribution license, the users are free to share (copy, distribute and transmit the contribution) and adapt (remix, transform, and build upon the material) the article for any purpose, provided they attribute the contribution in the manner specified by the author or licensor.
If the article was prepared jointly with other authors, the signatory of this form warrants that he/she has been authorized by all co-authors to sign this agreement on their behalf, and agrees to inform his/her co-authors of the terms of this agreement.