ON THE LEBESGUE SPACE OF VECTOR MEASURES

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
Keywords

INTEGRATION; L(1)

Citation

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, v.48, no.4, pp.779 - 789

ISSN
1015-8634
URI
http://hdl.handle.net/10203/7224
Appears in Collection
NE-Journal Papers(저널논문)
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