EXACT DIMENSIONALITY AND LEDRAPPIER-YOUNG FORMULA FOR THE FURSTENBERG MEASURE

Rapaport’s paper proves exact dimensionality and the Ledrappier–Young-type formulas (Theorem 1.3 parts (1)–(4)) via a careful, bespoke argument using Oseledets splittings, measurable partitions, and transverse dimension estimates; the statements and key constructions are explicit and coherent in the text. The model’s solution, by contrast, invokes a general “random Ledrappier–Young” theorem on a skew-product and claims invariance of projection-fiber partitions under the skew-product map, but that invariance fails (orthogonal complements do not commute with general linear maps), and the applicability of the cited general theorem is not justified for this non-uniformly contracting projective action. Hence the model’s proof outline is flawed/incomplete, while the paper’s proof is correct.