ON THE LEBESGUE SPACE OF VECTOR MEASURES

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In this paper we study the Banach space L(1)(G) of real valued measurable functions which are integrable with respect to a vector measure G in the sense of D. R. Lewis. First, we investigate conditions for a scalarly integrable function f which guarantee f is an element of L(1)(G). Next, we give a sufficient condition for a sequence to converge in L(1)(G). Moreover, for two vector measures F and G with values in the same Banach space, when F can be written as the integral of a function f is an element of L(1)(G), we show that certain properties of G are inherited to F; for instance, relative compactness or convexity of the range of vector measure. Finally, we give some examples of L(1)(G) related to the approximation property.
Publisher
Korean Mathematical Soc
Issue Date
2011
Language
ENG
Article Type
Article
Appears in Collection
NE-Journal Papers(저널논문)
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