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Macroscopic observables in a quantum spin system are given by sequences of spatial means of local elements $\frac{1}{2n+1}\sum_{j=-n}^n\gamma_j(A_{i}), \; n\in{\mathbb N},\; i=1,...,m$ in a UHF algebra.
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M. Rørdam, F. Larsen, N. Laustsen: An introduction to K-theory for C*-algebras
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