Asymptotic midpoint uniform convexity of a norm 
on an infinite-dimensional Banach space 
is positivity of its asymptotic two-sided midpoint modulus
for every 
. An averaged convention is
 |
where 
consists of the closed linear
subspaces of finite codimension.
The standard maximum-based modulus replaces the average of the two norms
by their maximum. If that modulus is 
, then 
, so the positivity conditions
agree. The property is abbreviated AMUC, and concerns the given norm;
existence of an equivalent asymptotically
uniformly convex norm is a separate question.
