The Upper Semi-Continuous Subadditive $\alpha$-Positively Homogeneous Functionals Defined on $S(\Omega,\Sigma,\mu)$ and $L^\beta(\Omega,\Sigma,\mu)$ |
Received:September 29, 2004 Revised:March 01, 2005 |
Key Words:
$S(\Omega,\Sigma,\mu)$ $L^\beta(\Omega,\Sigma,\mu)$ upper semi-continuous atom $\alpha$-convex.
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Fund Project:the National Natural Science Foundation of China (10571090); the Research Fund for the Doctoral Program of Higher Education (20010055013) |
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Abstract: |
This paper considers the non-existence of non-trivial upper semi-continuous subadditive $\alpha$-positively homogeneous functionals defined on $S(\Omega,\Sigma,\mu)$ and $L^\beta(\Omega,\Sigma,\mu)$. Some sufficient and necessary conditions are given. |
Citation: |
DOI:10.3770/j.issn:1000-341X.2007.01.023 |
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