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If ''f'' denotes the limit function, it follows that, for every ''n'' ≥ 0,
:<math>\max_{x \in [0, 1]} |f(x) - f_n(x)| \le 2^{-n+1} \, \max_{x \in [0, 1]} |f_1(x) -
Also the choice of starting function does not really matter, provided ''f''<sub>0</sub>(0) = 0, ''f''<sub>0</sub>(1) = 1 and ''f''<sub>0</sub> is [[Bounded function|bounded]]{{citation needed|date=
=== Fractal volume ===
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