Quasi-metric spaces with measure

Aleksandar Stojmirovic

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arXiv · math/0311070

Quasi-metric spaces with measure

Aleksandar Stojmirovic

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Abstract

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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BibTeX RIS

Aleksandar Stojmirovic. 2003-11-06. Quasi-metric spaces with measure. https://arxiv.org/abs/math/0311070

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