Rokhlin's multiple-mixing problem asks whether every invertible mixing transformation of a probability space, whose
inverse is a measurable function, is mixing
of every finite order. For measurable
sets 
, ..., 
, this would give
as 
through positive integers.
See also
Ergodic Theory,
Mixing
Transformation,
Multiple Ergodic Average
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References
Eisner, T.; Farkas, B.; Haase, M.; and Nagel, R. Operator Theoretic Aspects of Ergodic Theory. Cham, Switzerland: Springer, 2015. https://doi.org/10.1007/978-3-319-16898-2.Ryzhikov,
V. V. "Multiple Mixing, 75 Years of Rokhlin's Problem." 12 Nov 2024.
https://arxiv.org/abs/2411.07234.
Cite this as:
Weisstein, Eric W. "Rokhlin's Multiple-Mixing
Problem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RokhlinsMultiple-MixingProblem.html
Subject classifications
