## A study of convexity in normed linear spaces |

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39 is B-convex admissible measure Anatole Beck B-convex Banach space Beck's theorem cancellation Chapter choice choose closed under multiplication co(A convex hull convex NLS Corollary Define dense direct sum Dunford and Schwartz element indexed example exists finite dimensional hence B-convex Hilbert sum hypotheses i=1 Pi Pi+1 i=l i i i=l l l independent sequence integer isomorphic James large numbers law of large Lemma llxll llyll locally uniformly convex Math measure space N-sequence NLS's NORMED LINEAR SPACES open transformation Pick probability space Proof Q. E.D. Remarks real numbers refer to Theorem reflexive space resp satisfies property second conjugate sequence of real small jumps space of functions span strong law subspace sup extends Suppose thesis topology uniformly convex proper uniformly convex spaces unit ball unit sphere unit vectors valued random variables var(X X.ll z(cr