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Jul 10, 2013 at 15:49 comment added john mangual OK. When you rescale, the factor shrinks by $r^2$ so for 3 disjoint copies to fit in the original, $r_1^2 + r_2^2 + r_3^2 \leq 1$.
Jul 10, 2013 at 12:25 comment added Emil Jeřábek You need the images not to intersect, and all of them to fit in the original open set. The condition $r_1^2+r_2^2+r_3^2\le1$ is clearly necessary as long as $O$ has finite Lebesgue measure.
Jul 10, 2013 at 12:20 history answered john mangual CC BY-SA 3.0