Let f be a C~2 expanding map of the circle and μ=∫ρdm be the abso- lutely continuous invariant measure for this system. We formulate a model for a discrete approximation for μby perturbing the measure and then discretizing it. We show that whenever the distance δbetween lattice points of the discretization decays polynomially(but not linearly)in the perturbation parameter ε, then as εtends to 0, the discretized density converges of ρin a suitable Holder norm.
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