  We study the equivalence relation $R_N$ generated by the (non-free) action of
the generalized Thompson group $F_N$ on the unit interval. We show that this
relation is a standard, quasipreserving ergodic equivalence relation. Using
results of Feldman-Moore, Krieger and Connes we prove that the von Neumann
algebra $M(R_N)$ associated to $R_N$ is the hyperfinite type $III_{\lambda}$
factor, with $\lambda=1/N$.
