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