منابع مشابه
Closed Measure Zero Sets
We study the relationship between the σ-ideal generated by closed measure zero sets and the ideals of null and meager sets. We show that the additivity of the ideal of closed measure zero sets is not bigger than covering for category. As a consequence we get that the additivity of the ideal of closed measure zero sets is equal to the additivity of the ideal of meager sets.
متن کاملOn effectively closed sets of effective strong measure zero
The strong measure zero sets of reals have been widely studied in the context of set theory of the real line. The notion of strong measure zero is straightforwardly effectivized. A set of reals is said to be of effective strong measure zero if for any computable sequence {εn}n∈N of positive rationals, a sequence of intervals In of diameter εn covers the set. We observe that a set is of effectiv...
متن کاملFinite Powers of Strong Measure Zero Sets
In a previous paper – [17] – we characterized strong measure zero sets of reals in terms of a Ramseyan partition relation on certain subspaces of the Alexandroff duplicate of the unit interval. This framework gave only indirect access to the relevant sets of real numbers. We now work more directly with the sets in question, and since it costs little in additional technicalities, we consider the...
متن کاملMeasure zero sets with non - measurable sum
For any C ⊆ R there is a subset A ⊆ C such that A + A has inner measure zero and outer measure the same as C + C. Also, there is a subset A of the Cantor middle third set such that A+A is Bernstein in [0, 2]. On the other hand there is a perfect set C such that C + C is an interval I and there is no subset A ⊆ C with A + A Bernstein in I.
متن کاملOn Vector Sums of Measure Zero Sets
We consider the behaviour of measure zero subsets of a vector space under the operation of vector sum. The question whether the vector sum of such sets can be nonmeasurable is discussed in connection with the measure extension problem, and a certain generalization of the classical Sierpiński result [3] is presented. 2000 Mathematics Subject Classification: 28A05, 28D05.
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 1992
ISSN: 0168-0072
DOI: 10.1016/0168-0072(92)90001-g