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For every k N, let f₊: 1k+1, 1k 0, 1 be decreasing, linear functions such that f₊ (1k+1) = 1 and f₊ (1k) = 0, k = 1, 2,. We define the iterated function system S₍ by limiting the collection of functions f₊ to first n, meaning S₍ = \f₊ \₊=₁^n. Let J₍ denote the limit set of S₍. Then, ₍ P₇䂸 (J₍) = 2, where h₍ is the packing dimension of J₍ and P₇䂸 is the corresponding packing measure.
Rafał Tryniecki (Mon,) studied this question.