Rokhlin's multiple-mixing problem at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

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Rokhlin's multiple-mixing problem

at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

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Difficulty:	🧠🧠🧠🧠🧠	Ages:	13 - ∞
Skills:	things that move forever	Levels:	1
Category:	Dynamical systems and ergodic theory	Lean version:	YES! ✔
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Rokhlin’s multiple-mixing problem. Proves that every invertible mixing probability-preserving transformation is mixing of all finite orders, resolving Rokhlin's multiple-mixing problem for a single transformation. Correlations among any finite collection of measurable sets converge to the product of their measures whenever all pairwise time separations diverge.

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LEVEL 1 Rokhlin's multiple-mixing problem for one transformation

released 2026-09-23 | 1 theorem · 15 lemmas · 24 proofs · 18,236 words | PLAY LEVEL 1 » (pdf)

Every invertible mixing probability-preserving transformation is mixing of every finite order. Thus Rokhlin's multiple-mixing problem for a single transformation has an affirmative answer.

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