Типичные расширения эргодических систем

The paper proves that typical extensions do not preserve finite P-entropy by constructing, for a fixed vertical partition, a dense Gδ set of extensions whose P-entropy along a subsequence is uniformly bounded below, and then intersecting over a sequence of partitions with diverging entropy; this uses conjugation by a dense family of skew-products and an independence argument around equation (2), and is sound as written . The model’s proof attempts a different Rokhlin–tower block-correction scheme that could work in spirit, but it contains (i) a topological misstatement: it incorrectly asserts upper semicontinuity of h_P(R) implies the openness of {R: h_P(R)>m} (it would require lower semicontinuity), and (ii) a quantitative Baire-argument gap: the open dense sets U_{m,ℓ} are defined via a union over all partitions, which does not ensure, for a fixed partition, infinitely many j witnessing h_j(R,ξ)>m—needed to take limsup for that fixed ξ. These issues are fixable (e.g., fix one partition π_m per m and run a standard diagonal/Baire argument), but as written the model’s argument does not fully establish typicality. The paper’s argument remains correct and complete for Theorem 6.1.