Box-counting dimension in one-dimensional random geometry of multiplicative cascades

The uploaded paper proves exactly the box-dimension formula for f(E_a) under assumptions (1.2) and (1.8), see Theorem 1.10 (eq. (1.11)) with γ = −E(log_2 W) . The candidate solution correctly invokes this result and sketches the same two-step argument (E_α case, then transfer via eventual separation). Minor issues: it mislabels the cited theorem as “Theorem 1.12” (the PDF shows Theorems 1.9 and 1.10) and its moment condition should match (1.8), which (as stated in the paper) is used for the lower bound and entails the integrability needed for second derivatives . Apart from these cosmetic points, the model’s solution aligns with the paper.