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

Abstract

Assuming a separation property for Moran sets, we give a sufficient condition for thes0-dimensional upper and lower quantization coefficient for μ of order zero to be both positive and finite, when the quantization dimension exists and equals s0. For certain product measures associated with multiscale Moran sets, we determine the exact value s0 of the quantization dimension of order zero and present a subclass of such measures for which the s0-dimensional upper and lower quantization coefficient are both positive and finite. Several examples are constructed to illustrate the main results.