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In functional analysis, the class of ''B''-convex spaces is a class of Banach space. The concept of ''B''-convexity was defined and used to characterize Banach spaces that have the strong law of large numbers by Anatole Beck in 1962; accordingly, "B-convexity" is understood as an abbreviation of Beck convexity. Beck proved the following theorem: A Banach space is ''B''-convex if and only if every sequence of independent, symmetric, uniformly bounded and Radon random variables in that space satisfies the strong law of large numbers. Let ''X'' be a Banach space with norm || ||. ''X'' is said to be ''B''-convex if for some ''ε'' > 0 and some natural number ''n'', it holds true that whenever ''x''1, ..., ''x''''n'' are elements of the closed unit ball of ''X'', there is a choice of signs ''α''1, ..., ''α''''n'' ∈ such that : Later authors have shown that B-convexity is equivalent to a number of other important properties in the theory of Banach spaces. Being B-convex and having Rademacher type were shown to be equivalent Banach-space properties by Gilles Pisier. ==References== * * (See chapter 9) 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「B-convex space」の詳細全文を読む スポンサード リンク
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