Metric and Mixing Sufficient Conditions for Concentration of Measure
نویسنده
چکیده
We derive sufficient conditions for a family (Sn, ρn,Pn) of metric probability spaces to have the measure concentration property. Specifically, if the sequence {Pn} of probability measures satisfies a strong mixing condition (which we call η-mixing) and the sequence of metrics {ρn} is what we call Ψ-dominated, we show that (Sn, ρn,Pn) is a normal Lévy family. We establish these properties for some metric probability spaces, including the possibly novel S = [0, 1], ρn = ‖·‖1 case.
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