Izvorni znanstveni članak
A multidimensional generalization of the Steinhaus theorem
M. Crnjac
Sažetak
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.
Ključne riječi
measurable set; Lebesgue measure; outer Lebesgue measure; compact set; closed set
Hrčak ID:
1803
URI
Datum izdavanja:
20.12.1997.
Posjeta: 1.605 *