Conformal measure and decay of correlation for covering weighted systems

We show that for a large class of piecewise monotonic transformations on a totally ordered, compact set one can construct conformal measures and obtai n the exponential mixing rate for the associated equilibrium state. The met hod is based on the study of the Perron-Frobenius operator. The conformal m easure, the density of the invariant measure and the rate of mixing are ded uced by using an appropriate Hilbert metric, without an compactness argumen ts, even in the case of a countable to one transformation.