Haar systems, KMS states on von Neumann algebras and $C^{\ast }$-algebras on dynamically defined groupoids and Noncommutative Integration

Gilles G. de Castro, Artur O. Lopes, Gabriel Mantovani

We analyse certain Haar systems associated to groupoids obtained by certain natural equivalence relations of dynamical nature on sets like $\{1,2,...,d{\}}^{\mathbb{Z}}$, $\{1,2,...,d\…