The bounded vector measure associated to a conical measure and pettis differentiability

Journal of the Australian Mathematical Society

L. Rodriguez-Piazza¹ 

[1] M. C. Romero-Moreno

关键词: primary 46G10;    28B05;    47D50;   

DOI  :  10.1017/S1446788700002251

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

Let X be a locally convex space. Kluvánek associated to each X-valued countably additive vector measure a conical measure on X; this can also be done for finitely additive bounded vector measures. We prove that every conical measure u on X, whose associated zonoform Ku is contained in X, is associated to a bounded additive vector measure σ(u) defined on X, and satisfying σ(u)(H) ∈ H, for every finite intersection H of closed half-spaces. When X is a complete weak space, we prove that σ(u) is countably additive. This allows us to recover two results of Kluvánek: for any X, every conical measure u on it with Ku ⊆ X is associated to a countably additive X-valued vector measure; and every conical measure on a complete weak space is localizable. When X is a Banach space, we prove that σ(u) is countably additive if and only if u is the conical measure associated to a Pettis differentiable vector measure.

【 授权许可】

Unknown