Geodesic
The Banach-Saks Theorem in C(S)
Canadian journal of mathematics, Tome 26 (1974) no. 1, pp. 91-97

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A Banach space X has the Banach-Saks property if every sequence (xn ) in X converging weakly to x has a subsequence (xnk ) with (1/p)Σk=1 xnk converging in norm to x. Originally, Banach and Saks [2] proved that the spaces Lp (p > 1) have this property. Kakutani [4] generalized their result by proving this for every uniformly convex Banach space, and in [9] Szlenk proved that the space L 1 also has this property. 
Farnum, Nicholas R. The Banach-Saks Theorem in C(S). Canadian journal of mathematics, Tome 26 (1974) no. 1, pp. 91-97. doi: 10.4153/CJM-1974-009-9
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