On Meager Additive and Null Additive Sets in the Cantor Space 2ωand in R
نویسندگان
چکیده
منابع مشابه
Every null - additive set is meager - additive †
§1. The basic definitions and the main theorem. 1. Definition. (1) We define addition on 2 as addition modulo 2 on each component, i.e., if x, y, z ∈ 2 and x+ y = z then for every n we have z(n) = x(n) + y(n) (mod 2). (2) For A,B ⊆ 2 and x ∈ 2 we set x + A = {x + y : y ∈ A}, and we define A + B similarly. (3) We denote the Lebesgue measure on 2 with μ. We say that X ⊆ 2 is null-additive if for ...
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We develop a machinery which translates results on algebraic sums of sets of reals into the corresponding results on their cartesian product. Some consequences are: (1) The product of meager/null-additive sets in the Cantor space is meager/nulladditive, respectively. (2) The product of a meager/null-additive set and a strong measure zero/strongly meager set in the Cantor space has strong measur...
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ژورنال
عنوان ژورنال: Bulletin of the Polish Academy of Sciences Mathematics
سال: 2009
ISSN: 0239-7269,1732-8985
DOI: 10.4064/ba57-2-1