Haar meager sets revisited
نویسندگان
چکیده
منابع مشابه
Universally Meager Sets
We study category counterparts of the notion of a universal measure zero set of reals. We say that a set A ⊆ R is universally meager if every Borel isomorphic image of A is meager in R. We give various equivalent definitions emphasizing analogies with the universally null sets of reals. In particular, two problems emerging from an earlier work of Grzegorek are
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We show that it is consistent that the product of perfectly meager sets is perfectly meager.
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We will construct several models where there are no strongly meager sets of size 2 ℵ 0 .
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A set X ⊆ R is strongly meager if for every measure zero set H, X + H = R. Let SM denote the collection of strongly meager sets. We show that assuming CH, SM is not an ideal.
متن کاملNotes on Haar Null Sets
This informal set of notes contains some of the new results which will appear in the author’s 2013 dissertation. We show that every infinite product of locally compact non-compact groups decomposes into the disjoint union of a Haar null set and a meager set, which gives a partial positive answer to a question of Darji. We also show that the compact sets in each such product group are always Haa...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2016
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2016.03.065