<abstract xmlns="http://www.w3.org/1999/xhtml"><p> Let I be a proper σ-ideal of subsets of the real line. In a σ-field of Borel sets modulo sets from the σ-ideal I we introduce an analogue of the saturated non-measurability considered by Halperin. Properties of (B∆I,I)-saturated sets are investigated.</p><p>M. Kuczma considered a problem how small or large a Hamel basis can be. We try to study this problem in the context of sets from I.</p></abstract>

Let I be a proper σ-ideal of subsets of the real line. In a σ-field of Borel sets modulo sets from the σ-ideal I we introduce an analogue of the saturated non-measurability considered by Halperin. Properties of (B∆I,I)-saturated sets are investigated.M. Kuczma considered a problem how small or large a Hamel basis can be. We try to study this problem in the context of sets from I.

(B∆I,I)-saturated sets and Hamel basis

University of Łódź Faculty of Mathematics and Computer Science ul. Banacha 22 PL-90-238 Łódź

University of Łódź Faculty of Mathematics and Computer Science ul. Banacha 22 PL-90-238 Łódź POLAND

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"(B∆I,I)-saturated sets and Hamel basis"}

Let I be a proper σ-ideal of subsets of the real line. In a σ-field of Borel sets modulo sets from the σ-ideal I we introduce an analogue of the saturated...

(B∆I,I)-saturated sets and Hamel basis

Online veröffentlicht: 25. Sept. 2015

Seitenbereich: 143 - 150

Eingereicht: 28. Nov. 2014

DOI: https://doi.org/10.1515/tmmp-2015-0011

© 2015

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.