Products of special sets of real numbers

Boaz Tsaban, Tomasz Weiss

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


We describe a simple 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 a meager/null-additive set and a strong measure zero/strongly meager set in the Cantor space has strong measure zero/is strongly meager, respectively. 2. Using Scheepers' notation for selection principles: Sfin(Ω, Ωgp) ∩ S1(O,O) = S1(Ω, Ωgp), and Borel's Conjecture for S1(Ω, Ω) (or just S1(Ω,Ωgp)) implies Borel's Conjecture. These results extend results of Scheepers and Miller, respectively.

Original languageEnglish
Pages (from-to)819-836
Number of pages18
JournalReal Analysis Exchange
Issue number2
StatePublished - 2004
Externally publishedYes


  • Products
  • Special sets of real numbers


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