LEBESGUE MEASURE OF PARTS FOR R(X)
LEBESGUE MEASURE OF PARTS FOR R(X)
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R(X) 部分的勒贝格测度
DOI：
10.1090/s0002-9939-1967-0216297-8
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发表时间：
1967
期刊：
影响因子：
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通讯作者：
D. Wilken
中科院分区：
文献类型：
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作者：
D. Wilken
1. 介绍。让X是一个紧集在复平面由R C (X)是函数代数由函数由rational统一在X可逼近的函数的两极之外X R (X)是C (X)的子代数,所有复杂的价值连续函数的代数X,和的最大理想空间R与X (X)可以确定在这个报告中我们检查的性质格里森R (X)和获得的结果每个重要的部分都有积极的平面勒贝格测度,每个平凡部分都是一个峰值点。？2包含关于格里森部分的定义和事实的简要总结，并表示与后来的证明相关的措施。在吗?主要结果和一些值得注意的结果是确定的。的结束语？4主要针对的是R(X)部分的许多未经证实但推测的性质。
1. Introduction. Let X be a compact set in the complex plane C. By R(X) is meant the function algebra which consists of functions uniformly approximable on X by rational functions whose poles lie outside X. Then R(X) is a subalgebra of C(X), the algebra of all complex valued continuous functions on X, and the maximal ideal space of R(X) can be identified with X. In this note we examine the nature of the Gleason parts of R(X) and obtain the result that each nontrivial part has positive planar Lebesgue measure, and each trivial part is a peak point. ?2 contains a brief summary of the definitions and facts about Gleason parts and representing measures which are relevant to the later proofs. In ?3 the main result is established along with some noteworthy consequences. The concluding remarks of ?4 are directed primarily at the numerous unproven but conjectured properties of the parts of R(X).