Realizing homomorphisms of category algebras
Extremal preimage measures and measurable weak sections
A survey on lifting in measure theory
Selected results on measurable selections
Induced ...-Homomorphisms and a Parametrization of Measurable Sections via Extremal Preimage Measures.
On Bandt's Tangential Distribution for Self-Similar Measures.
A selection theorem for Boolean correspondences.
A Radon-Nikodym theorem for capacities.
Distortion mismatch in the quantization of probability measures
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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