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Mathematical Communications, Vol. 2 No. 2, 1997.

Original scientific paper

A multidimensional generalization of the Steinhaus theorem

M. Crnjac

Full text: english pdf 139 Kb

page 129-133

downloads: 1.118

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Abstract

Steinhaus has shown that the subset of $\R$ of the form A+B={a+b:a\in A,b\in B\}contains an interval provided both sets $A\in\R$ and $B\in\R$ have positive Lebesgue measure.
In the present paper the author generalizes this fact to subsets of
$\R^n$, $n\in N$, satisfying the above conditions. The statement is proved in a new way using a very interesting lemma.

Keywords

measurable set; Lebesgue measure; outer Lebesgue measure; compact set; closed set

Hrčak ID:

1803

URI

https://hrcak.srce.hr/1803

Publication date:

20.12.1997.

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