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.
