# Milman–Pettis theorem

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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.

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