Quasi-metric spaces with measure

Details Quasi-metric spaces with measure Quasi-metric spaces with measure

2003-11-06

arxiv.org/abs/math/0311070v1

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

Mathematics

General Topology

17 pages

Scientific paper

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.

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