On a rectangle inclusion problem
Author:
Janusz Pawlikowski
Journal:
Proc. Amer. Math. Soc. 123 (1995), 31893195
MSC:
Primary 03E05; Secondary 03E15, 54A35
MathSciNet review:
1264828
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Abstract: We show that if every set of reals of size contains a meagertoone continuous image of a set that cannot be covered by less than meager sets, then there exists a null (Lebesgue measure zero) subset of the plane that meets every nonnull rectangle . The antecedent is satisfied, e.g., if Cohen reals are added to a model of the continuum hypothesis.
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 M. Burke, A theorem of Friedman on rectangle inclusion and its consequences, Note of March 7, 1991.
 [2]
 T. Bartoszyński, M. Goldstern, H. Judah, and S. Shelah, All meager filters may be null, Proc. Amer. Math. Soc. 117 (1993), 515521. MR 1111433 (93d:03055)
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 T. Bartoszyński and H. Judah, Measure and category in set theory (forthcoming book).
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 H. G. Eggleston, Two measure properties of cartesian product sets, Quart. J. Math. Oxford (2) 5 (1954), 108115. MR 0064850 (16:344e)
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 D. H. Fremlin, Problem list, circulated notes, 1987.
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 D. H. Fremlin and M. Talagrand, A decomposition theorem for additive set functions and applications to Pettis integral and ergodic means, Math. Z. 168 (1979), 117142. MR 544700 (80k:28004)
 [7]
 A. Miller, Some properties of measure and category, Trans. Amer. Math. Soc. 266 (1981), 93114. MR 613787 (84e:03058a)
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 , Mapping a set of reals onto the reals, J. Symbolic Logic 48 (1983), 575584. MR 716618 (84k:03125)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199512648289
PII:
S 00029939(1995)12648289
Keywords:
Subsets of the plane,
nonnull rectangles,
closed null sets
Article copyright:
© Copyright 1995
American Mathematical Society
