Uniformly convex space

Summary

A normed space is uniformly convex when midpoints of two unit vectors that are far apart lie uniformly deep inside the unit ball. It is a quantitative form of strict convexity of the unit ball. Hilbert spaces and $L^p$ spaces for $1 < p < \infty$ are uniformly convex, and the Milman–Pettis theorem says that every uniformly convex Banach space is reflexive.