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- B-convex_space abstract "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 x1, ..., xn are elements of the closed unit ball of X, there is a choice of signs α1, ..., αn ∈ {−1, +1} such thatLater 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.".
- B-convex_space wikiPageID "21600196".
- B-convex_space wikiPageRevisionID "448309601".
- B-convex_space hasPhotoCollection B-convex_space.
- B-convex_space subject Category:Banach_spaces.
- B-convex_space subject Category:Convex_geometry.
- B-convex_space subject Category:Probability_theory.
- B-convex_space type Abstraction100002137.
- B-convex_space type Attribute100024264.
- B-convex_space type BanachSpaces.
- B-convex_space type Space100028651.
- B-convex_space comment "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.".
- B-convex_space label "B-convex space".
- B-convex_space sameAs m.05mv1lr.
- B-convex_space sameAs Q4833724.
- B-convex_space sameAs Q4833724.
- B-convex_space sameAs B-convex_space.
- B-convex_space wasDerivedFrom B-convex_space?oldid=448309601.
- B-convex_space isPrimaryTopicOf B-convex_space.