$\varphi$信封的实现集和泛型属性

Pub Date : 2019-06-17 DOI:10.7146/MATH.SCAND.A-110766

A. Cabot, A. Jourani, L. Thibault, D. Zagrodny

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引用次数: 1

摘要

研究了函数在给定点上$\varphi$-包络的可达集。将函数的闭凸包的$\varphi$包络的可达集包含到函数的可达集中，是在足够通用的设置中保留的，以包含$\varphi$是不小于$1$幂的范数的情况。在几个基本情况下，在给定空间的泛型子集上保证了可达集的非空性。

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The attainment set of the $\varphi$-envelope and genericity properties

The attainment set of the $\varphi$-envelope of a function at a given point is investigated. The inclusion of the attainment set of the $\varphi$-envelope of the closed convex hull of a function into the attainment set of the function is preserved in sufficiently general settings to encompass the case $\varphi$ being a norm in a power not less than $1$. The non-emptiness of the attainment set is guaranteed on generic subsets of a given space, in several fundamental cases.

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