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On the Theory of Vector Measures

William Howard Graves

出版	American Mathematical Soc., 1977
主題	Mathematics / GeneralMathematics / Vector Analysis
ISBN	08218219549780821821954
URL	http://books.google.com.hk/books?id=_grUCQAAQBAJ&hl=&source=gbs_api
EBook	SAMPLE

註釋

Given a ring of subsets of a non-empty set, there is a universal measure on the ring with values in an associated complete locally convex space which carries, through its typology, much of the combinatorial and measure theoretic structure of the ring. Moreover, vector measures of the ring are in 1-1 correspondence with continuous linear maps on the associated space. Several aspects of the theory of vector measures including decomposition theorems, extension theorems, Bartle-Dunford-Schwartz type theorems on weak compactness, and Pettis and Orlicz-Pettis-type theorems are studied in the unifying context of the universal measure and the associated universal representation theorem. A brief account of a similar theory for measures on abstract Boolean algebras is also given.