Invariant ideals and Borel sets
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- by Andrzej Pelc
- Proc. Amer. Math. Soc. 97 (1986), 503-506
- DOI: https://doi.org/10.1090/S0002-9939-1986-0840637-1
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Abstract:
We investigate the size of the algebra $\mathcal {B}(I)$, where $\mathcal {B}$ is the family of Borel sets and $I$ is a translation invariant ideal of sets of reals. In particular the question whether $\mathcal {B}(I)$ can contain Vitali selectors or even all sets of reals is discussed in connection with the completeness of $I$ and its invariance.References
- J. Brzuchowski and J. Cichoń, Miara $i$ kategoria, unpublished.
- D. A. Martin and R. M. Solovay, Internal Cohen extensions, Ann. Math. Logic 2 (1970), no. 2, 143–178. MR 270904, DOI 10.1016/0003-4843(70)90009-4 A. Pele, Invariant measures and ideals on discrete groups, Dissertationes Math. (in print).
- C. Ryll-Nardzewski and R. Telgársky, The nonexistence of universal invariant measures, Proc. Amer. Math. Soc. 69 (1978), no. 2, 240–242. MR 466494, DOI 10.1090/S0002-9939-1978-0466494-9 A. Taylor, On the cardinality of the algebra $\mathcal {P}(k)/I$, handwritten notes.
Bibliographic Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 97 (1986), 503-506
- MSC: Primary 04A15; Secondary 03E05, 28A05
- DOI: https://doi.org/10.1090/S0002-9939-1986-0840637-1
- MathSciNet review: 840637