Valuations on Lp-Spaces

被引：32
|
作者：
Tsang, Andy [1 ]
机构：
[1] NYU, Dept Math, Polytech Inst, Brooklyn, NY 11201 USA
来源：
INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2010年 / 2010卷 / 20期
关键词：
INVARIANT VALUATIONS; CONVEX-SETS; MANIFOLDS; BODIES;
D O I：
10.1093/imrn/rnq028
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A representation theorem is established for continuous valuations on L-p-spaces whose underlying measure is non-atomic. As a consequence, a complete classification is obtained of continuous translation invariant valuations on L-p(R-n) and of continuous rotation invariant valuations on L-p(Sn-1).
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页码：3993 / 4023
页数：31
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