Modulus and characteristic of convexity: Difference between revisions

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In [[mathematics]], the '''modulus and characteristic of convexity''' are measures of "how [[convex set|convex]]" the [[unit ball]] in a [[Banach space]] is. In some sense, the modulus of convexity has the same relationship to the ''ε''-''δ'' definition of [[uniformly convex space|uniform convexity]] as the [[modulus of continuity]] does to the ''ε''-''δ'' definition of [[continuous function|continuity]].

==Definitions==

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* [[Vitali Milman|Vitali D. Milman]]. Geometric theory of Banach spaces II. Geometry of the unit sphere. ''Uspechi Mat. Nauk,'' vol. 26, no. 6, 73-149, 1971; ''Russian Math. Surveys'', v. 26 6, 80-159.

* {{ cite articlejournal | last=Pisier |first=Gilles |authorlink=Gilles Pisier | title= Martingales with values in uniformly convex spaces | journal=Israel J. Math. | volume=20 | year=1975 | number=3-4 | pages=326–350 | doi = 10.1007/BF02760337 | url=http://www.springerlink.com/content/y0176lm220h756k6 | id={{MR|394135}}|}}

[[Category:Banach spaces]]