Topology Proceedings 28 No. 2 (2004), pp. 655-671

Quasi-metric spaces with measure

Aleksandar Stojmirovic

The phenomenon of concentration of measure on high dimensional structures is usually stated in terms of a metric space with a Borel measure, also called an mm-space. We extend some of the mm-space concepts to the setting of a quasi-metric space with probability measure (pq-space). Our motivation comes from biological sequence comparison: we show that many common similarity measures on biological sequences can be converted to quasi-metrics. We show that a high dimensional pq-space is very close to being an mm-space.

Keywords: quasi-metrics, concentration of measure, biological sequences

Mathematics Subject Classification: 54E55, 28C15 (92C40)

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Topology Proceedings, Volume 28, No. 2 (2004)
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