#### Glasnik Matematicki, Vol. 32, No.2 (1997), 207-212.

### ON A RESULT OF M. KUCZMA

### Harry I. Miller, Franz J. Schnitzer and
Henry L. Wyzinski

Department of Mathematics, University of Tennessee at Chattanooga,
Chattanooga, Tenessee 37403, USA

Department of Mathematics, Montanuniversitat, A-8700 Leoben,
Austria

Department of Mathematics, Indiana University N. W., Gary, IN 46408,
USA

**Abstract.** M. Kuczma proved that if *A* is a set of
reals having positive Lebesgue measure then *A* has a subset
*A*' such that *A*' has positive Lebesgue measure
and is symmetric about a point. We consider similar
questions regarding other classes of sets (other then the class
of sets having positive Lebesgue measure). In addition, other
results and remarks concerning several classes of sets are presented.

**1991 Mathematics Subject Classification.**
28A05, 39B05.

**Key words and phrases.** Symmetric sets, Bernstein sets,
Hamel bases, positive Lebesgue measure, Baire property, additive
functions.

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