Abstract

We estimate the observable diameter of the lp-product space Xn of an mm-space X by using the limit formula in our previous paper (Ozawa and Shioya, Math. Zeit. (to appear)). The idea of our proof is based on Gromov’s book (In: Metric structures for Riemannian and non-Riemannian spaces, 2007). As a corollary we obtain the phase transition property of \({\{X^n\}_{n=1}^\infty}\) under a uniform discreteness condition.

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