We present results for the equation of state for pure SU(3) gauge theory obtained with a renormalization-group (RG) improved action. The energy density and pressure are calculated on a $16^3times 4$ and a $32^3times 8$ lattice employing the integral method. Extrapolating the results to the continuum limit, we find the energy density and pressure to be in good agreement with those obtained with the standard plaquette action within the error of 3-4%.
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