  We elucidate the asymptotics of the L^s-quantization error induced by a
sequence of L^r-optimal n-quantizers of a probability distribution P on R^d
when s>r. In particular we show that under natural assumptions, the optimal
rate is preserved as long as s<r+d (and for every s in the case of a compactly
supported distribution). We derive some applications of these results to the
error bounds for quantization based quadrature formulae in numerical
integration on R^d and on the Wiener space.
