1. ON BOREL MAPS, CALIBRATED s-IDEALS, AND HOMOGENEITY.
- Author
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POL, R. and ZAKRZEWSKI, P.
- Subjects
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BOREL subgroups , *MATHEMATICAL analysis , *LATTICE theory , *MATHEMATICS theorems , *ALGEBRA - Abstract
Let μ be a Borel measure on a compactum X. The main objects in this paper are s-ideals Ipdimq, J0pμq, Jf pμq of Borel sets in X that can be covered by countably many compacta which are finite-dimensional, or of μ-measure null, or of finite μ-measure, respectively. Answering a question of J. Zapletal, we shall show that for the Hilbert cube, the s-ideal Ipdimq is not homogeneous in a strong way. We shall also show that in some natural instances of measures μ with nonhomogeneous s-ideals J0pμq or Jf pμq, the completions of the quotient Boolean algebras BorelpXq{J0pμq or BorelpXq{Jf pμq may be homogeneous. We discuss the topic in a more general setting, involving calibrated s-ideals. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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