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ON THE LEBESGUE SPACE OF VECTOR MEASURES
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 Title & Authors
ON THE LEBESGUE SPACE OF VECTOR MEASURES
Choi, Chang-Sun; Lee, Keun-Young;
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 Abstract
In this paper we study the Banach space (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 (G). Next, we give a sufficient condition for a sequence to converge in (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 (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 (G) related to the approximation property.
 Keywords
Lebesgue space of vector measure;convergence in (G);the range of vector measures;Lyapunov convexity theorem;the approximation property;
 Language
English
 Cited by
 References
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