In mathematics, the Milman–Pettis theorem states that every uniformly convex Banach space is reflexive.
The theorem was proved independently by D. Milman (1938) and B. J. Pettis (1939).
S. Kakutani gave a different proof in 1939, and John R. Ringrose published a shorter proof in 1959.
Mahlon M. Day (1941) gave examples of reflexive Banach spaces which are not isomorphic to any uniformly convex space.