[proofplan] This entry records a problem statement rather than an assertion with a proof. We verify that the formulation is well-defined by spelling out the two mixing notions and observing that the displayed conclusion is precisely mixing of all orders. [/proofplan] [step:Identify the hypothesis] The hypothesis displayed in the statement is the usual two-fold strong mixing condition: \begin{align*} \mu(T^{-n}A\cap B)\to\mu(A)\mu(B) \end{align*} for all measurable sets $A$ and $B$. [/step] [step:Identify the conclusion being asked about] For a fixed $r\geq2$, mixing of order $r+1$ requires asymptotic independence of $r+1$ time-separated events. Writing the time differences as gaps $n_1,\ldots,n_r$ gives exactly \begin{align*} \mu\left(A_0\cap T^{-n_1}A_1\cap\cdots\cap T^{-(n_1+\cdots+n_r)}A_r\right) \to \prod_{j=0}^r\mu(A_j) \end{align*} as all gaps tend to infinity. [/step] [step:Conclude that this is a problem formulation] The statement therefore asks whether two-fold strong mixing forces mixing of order $r+1$ for every $r\geq2$. That question is Rokhlin's multiple-mixing problem. Since the content of this entry is the formulation of the problem, no further theorem is asserted here. [/step]