Definition:Balanced Set

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Let $\Bbb F \in \set {\R, \C}$.

Let $X$ be a vector space over $\Bbb F$.

Let $A \subseteq X$.

We say that $A$ is balanced if and only if:

$s A \subseteq A$ for all $s \in \Bbb F$ with $\cmod s \le 1$

where $s A$ is the dilation of $A$ by $s$.

Also see

  • Results about balanced sets can be found here.