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In this note we make a very elementary technical observation to the effectthat Ruelle's construction of the thermodynamic limit of the classical entropydensity defined with a regularized microcanonical measure actually establishesthe thermodynamic limit for the entropy density defined with the propermicrocanonical measure. At this stage a key formula is still derived from theregularized measures. We also show that with only minor changes in the proofthe regularization of the microcanonical measure is actually not needed at all.

On Ruelle's construction of the thermodynamic limit for the classical microcanonical entropy