= Modified Cantor set with telescoping remaining lengths
{c}
{title2=$L_n=\frac13+\frac{2}{3\cdot2^n}$}
Starting from $[0,1]$, remove the central fraction $1/(2^n+2)$ of every stage-$n$ interval. The total length obeys $L_{n+1}/L_n=(2^n+1)/(2^n+2)$, which telescopes to the displayed value. The limiting intersection has <Lebesgue outer measure> at most $1/3$ by covering it with the stage intervals and slightly enlarging them to open intervals. This argument uses no integration.
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