Let E be a Moran set on R1 associated with a bounded closed interval J and two sequences (nk)k=1∞ and (Ck=(ck,j)j=1nk)k ≥ 1. Let μ be the Moran measure on E associated with a sequence (Pk)k ≥ 1 of positive probability vectors with Pk=(pk,j)j=1nk, k ≥ 1. We assume that
For every n ≥ 1, let αn be an n optimal set in the quantization for μ of order r ∈ (0, ∞) and {Pa(αn)}a∈αn an arbitrary Voronoi partition with respect to αn. We write
We show that J(αn, μ), J(αn, μ) and en,rr (μ) -en+1,rr(μ) are of the same order as 1/n en,rr (μ), where en,rr (μ):=∫ d(x, αn)rdμ(x) is the nth quantization error for μ of order r. In particular, for the class of Moran measures on R1, our result shows that a weaker version of Gersho's conjecture holds.