Expected Maharam-Types and Lyapunov's Theorem for Vector Measures on Banach Spaces
Expected Maharam-Types and Lyapunov's Theorem for Vector Measures on Banach Spaces
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Banach 空间上矢量测度的预期 Maharam 类型和 Lyapunov 定理
DOI：
10.1215/ijm/1403534490
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
Nobusumi Sagara
中科院分区：
文献类型：
--
作者：
M. A. Khan;Nobusumi Sagara
This paper offers a sufficient condition, based on Maharam (1942) and re-emphasized by Hoover-Keisler (1984), for the validity of Lyapunov's (1940) theorem on the range of an atomless vector measure taking values in an infinite-dimensional Banach space that is not necessarily separable nor has the RNP property. In particular, we obtain an extension of a corresponding result due to Uhl (1969). The proposed condition is also shown to be necessary in the sense formalized in Keisler-Sun (2009), and thereby closes a question of long-standing as regards an infinite-dimensional generalization of the theorem. The result is applied to obtain short simple proofs of recent results on the convexity of the integral of a set-valued function, and on the characterization of restricted cores of a saturated economy.
