The translative covering number 
of sets in a vector
space is the least number of translates of 
whose union contains 
:
 |
The centers 
need not lie in 
. When no finite cover exists, the
covering number is infinite. For a bounded set
in a metric vector space, 
, where 
is the unit ball, is a metric
entropy at scale 
. This covering notion differs from the measure-theoretic
entropy of a dynamical system. The metric
entropy duality conjecture compares covering numbers of convex
bodies and their polar bodies.
