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Let $X=X_1\times X_2$ and $Y=Y_1\times Y_2$ and $(X_i,Y_i)$ are interpolation couple. Then it seems obvious that $$ [X,Y]_{\theta}=[X_1,Y_1]_\theta \times [X_2,Y_2]_\theta $$ for every $\theta\in (0,1)$. Is there any reference for this result. I have checked many books. But, it seems that nobody state it.

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