[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.2011.48.4.779

ON THE LEBESGUE SPACE OF VECTOR MEASURES

Choi, Chang-Sun (Department of Mathematical Sciences KAIST)
Lee, Keun-Young (Department of Advanced Technology Fusion Konkuk University)

Publication Information

Bulletin of the Korean Mathematical Society / v.48, no.4, 2011 , pp. 779-789 More about this Journal

Abstract

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 $f{\in}L^1$ (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 $f{\in}L^1$ (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.

Keywords

Lebesgue space of vector measure; convergence in $L^1$ (G); the range of vector measures; Lyapunov convexity theorem; the approximation property;

Citations & Related Records

Times Cited By Web Of Science : 0 (Related Records In Web of Science)
Times Cited By SCOPUS : 0

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