In such disparate contexts as the Hahn-Banach theorem, seminorms, Kol-mogorov’s theorem (cf. 6.162), von Neumann’s theory of almost periodic functions on groups (cf. 2.93), his theory of games [NM] and linear programming, Jensen’s inequality, Hadamard’s three-lines/three-circles theorems, the Hausdorff-Young theorem, probability theory, etc., the rôle played by convexity is central. The following discussion attempts to illustrate that role in complex analysis.
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