Aequationes mathematicae

, Volume 39, Issue 1, pp 55–67 | Cite as

On a question of H. Kraljević

  • Miljenko Crnjac
  • Boris Guljaš
  • Harry I. Miller
Research Papers


In this paper, assuming a certain set-theoretic hypothesis, a positive answer is given to a question of H. Kraljević, namely it is shown that there exists a Lebesgue measurable subsetA of the real line such that the set {c ∈ R: A + cA contains an interval} is nonmeasurable. Here the setA + cA = {a + ca′: a, a′ ∈ A}. Two other results about sets of the formA + cA are presented.

AMS (1980) subject classification

Primary 28A05 


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Copyright information

© Birkhäuser Verlag 1990

Authors and Affiliations

  • Miljenko Crnjac
    • 1
    • 2
    • 3
  • Boris Guljaš
    • 1
    • 2
    • 3
  • Harry I. Miller
    • 1
    • 2
    • 3
  1. 1.OsijekYugoslavia
  2. 2.Dept. of MathematicsUniversity of ZagrebZagrebYugoslavia
  3. 3.SarajevoYugoslavia

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