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  1. Marek Balcerzak, Barnabás Farkas & Szymon Gła̧b (2013). Covering Properties of Ideals. Archive for Mathematical Logic 52 (3-4):279-294.
    Elekes proved that any infinite-fold cover of a σ-finite measure space by a sequence of measurable sets has a subsequence with the same property such that the set of indices of this subsequence has density zero. Applying this theorem he gave a new proof for the random-indestructibility of the density zero ideal. He asked about other variants of this theorem concerning I-almost everywhere infinite-fold covers of Polish spaces where I is a σ-ideal on the space and the set of indices (...)
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  2. Marek Balcerzak & Tomasz Filipczak (2011). On Monotone Hull Operations. Mathematical Logic Quarterly 57 (2):186-193.
    We extend results of Elekes and Máthé on monotone Borel hulls to an abstract setting of measurable space with negligibles. This scheme yields the respective theorems in the case of category and in the cases associated with the Mendez σ-ideals on the plane. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
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  3. Marek Balcerzak, Andrzej Roslanowski & Saharon Shelah (1998). Ideals Without CCC. Journal of Symbolic Logic 63 (1):128-148.
    Let I be an ideal of subsets of a Polish space X, containing all singletons and possessing a Borel basis. Assuming that I does not satisfy ccc, we consider the following conditions (B), (M) and (D). Condition (B) states that there is a disjoint family F $\subseteq$ P(X) of size c, consisting of Borel sets which are not in I. Condition (M) states that there is a Borel function f: X → X with $f^{-1}[\{x\}] \not\in$ I for each x ∈ (...)
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  4. Marek Balcerzak, Krzysztof Ciesielski & Tomasz Natkaniec (1997). Sierpiński-Zygmund Functions That Are Darboux, Almost Continuous, or Have a Perfect Road. Archive for Mathematical Logic 37 (1):29-35.
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