International Conference «Mathematical and Informational Technologies, MIT-2011»
(IX Conference «Computational and Informational Technologies for Science,
Engineering and Education»)

Vrnjacka Banja, Serbia, August, 27–31, 2011

Budva, Montenegro, August, 31 – September, 5, 2011

Arandelovic I.   Krtinic D.  

An extension of Steinhaus’s theorem

Reporter: Arandelovic I.

     In 1920 H. Steinhaus (H. Steinhaus, Sur les distances des points de mesure positive, Fund. Math. 1 (1920) 93-104) proved the following result: ‘Let A be a Lebesgue measurable set of a positive measure. Then in A exist at least two points such that distance between them is a rational number.’
      In this paper (talk) we shall proved that in A exists sequences (xn) of different points such that distance between any of its members is a rational number.

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