feat: add Ornstein–Weiss ℤᵈ Rokhlin lemma eval problem#309
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§109 of Knill's "Some Fundamental Theorems in Mathematics" (additional statement; the boxed main theorem is the classical Rokhlin lemma). The multidimensional generalization (Ornstein–Weiss, 1987): for every free measure-preserving ℤᵈ-action T on a standard Borel probability space, every box size N ≥ 1, and every ε > 0, there is a measurable base B such that the translates T v '' B for v ∈ [0, N)ᵈ are pairwise disjoint with measure ≥ 1 - ε. Mathlib has the supporting measure theory and Finset / box machinery but no multidimensional Rokhlin lemma and no free measure-preserving ℤᵈ-actions. Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
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This PR adds an eval problem for the Ornstein–Weiss
ℤᵈRokhlinlemma (Ornstein–Weiss, 1987): the multidimensional generalization of
the classical Rokhlin lemma. For every free measure-preserving
ℤᵈ-actionTon a standard Borel probability space (withd ≥ 1,identity axiom
T 0 = id, and the homomorphism axiom), every box sizeN ≥ 1, and everyε > 0, there is a measurable baseBsuch thatthe translates
T v '' Bforv ∈ [0, N)ᵈare pairwise disjointwith measure
≥ 1 − ε. Additional statement of §109 of Knill'sSome Fundamental Theorems in Mathematics (the boxed main theorem
is the classical Rokhlin lemma).
Mathlib has
MeasurePreserving,IsProbabilityMeasure,Set.PairwiseDisjoint,Fintype.piFinset,Finset.Ico, andStandardBorelSpace, but no Ornstein–Weiss lemma, no freemeasure-preserving
ℤᵈ-actions, no multidimensional Rokhlin towers.The Challenge ships two small helper definitions (
IsFreeActionandboxShape).No formalization found in any major prover.
🤖 Prepared with Claude Code