Asymptotics of the geometric mean error in the quantization for product measures on Moran sets

Assuming a separation property for Moran sets, we give a sufficient condition for the s 0 -dimensional upper and lower quantization coefficient for μ of order zero to be both positive and finite, when the quantization dimension exists and equals s 0 . For certain product measures associated with multiscale Moran sets, we determine the exact value s 0 of the quantization dimension of order zero and present a subclass of such measures for which the s 0 -dimensional upper and lower quantization coefficient are both positive and finite. Several examples are constructed to illustrate the main results.