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We continue in this article the study of laminations dual to very smallactions of a free group F on R-trees. We prove that this lamination determinescompletely the combinatorial structure of the R-tree (the so-called observers'topology). On the contrary the metric is not determined by the lamination, andan R-tree may be equipped with different metrics which have the same observers'topology.

Non-unique ergodicity, observers' topology and the dual algebraic lamination for $\R$-trees