Original scientific paper
A multidimensional generalization of the Steinhaus theorem
M. Crnjac
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
Publication date:
20.12.1997.
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