  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.
