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Abstract Let ν be a Borel probability measure on ℝ d R^{d} and q, t ∈ ℝ q, t. This study takes a broad approach to the multifractal and fractal analysis problem and proposes an intrinsic definition of the general Hausdorff and packing measures by taking into account sums of the type ∑ i h - 1 (q h (ν (B (x i, r i) ) ) + t g (r i) ) ₈h^-1 (qh ( (B (x₈, r₈) ) ) +tg (r₈) ) for some prescribed functions h and g. The aim of this paper is to study the descriptive set-theoretic complexity and measurability of these measures and related dimension maps.
Selmi et al. (Tue,) studied this question.
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