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.  
Fund Project:the National Natural Science Foundation of China (10571090); the Research Fund for the Doctoral Program of Higher Education (20010055013)
Author NameAffiliation
FU Xiao-hong Department of Mathematics, Jiaying College, Guangdong 514015, China
Department of Mathematics, Nankai University, Tianjin 300071, China 
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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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