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摘要翻译：
给出了本质有界随机变量空间上具有Lebesgue性质（序连续性）的单调凸函数，将其推广到尽可能大的随机变量实体向量空间。我们证明了这种扩张存在一个显式构造的极大值，其中扩张的极大域是自然Orlicz型空间的一个（可能适当的）子空间，具有一定的一致可积性。作为应用，我们利用一致可积性给出了任意随机变量实空间上单调凸函数的Lebesgue性质的刻划，并给出了该函数的一个“nice”对偶表示。
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英文标题：
《Maximum Lebesgue Extension of Monotone Convex Functions》
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作者：
Keita Owari
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最新提交年份：
2014
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分类信息：
一级分类：Mathematics 数学
二级分类：Functional Analysis 功能分析
分类描述：Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory
Banach空间，函数空间，实函数，积分变换，分布理论，测度理论
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一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Quantitative Finance 数量金融学
二级分类：Risk Management 风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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英文摘要：
Given a monotone convex function on the space of essentially bounded random variables with the Lebesgue property (order continuity), we consider its extension preserving the Lebesgue property to as big solid vector space of random variables as possible. We show that there exists a maximum such extension, with explicit construction, where the maximum domain of extension is obtained as a (possibly proper) subspace of a natural Orlicz-type space, characterized by a certain uniform integrability property. As an application, we provide a characterization of the Lebesgue property of monotone convex function on arbitrary solid spaces of random variables in terms of uniform integrability and a "nice" dual representation of the function.
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PDF链接：
https://arxiv.org/pdf/1304.7934
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