If \(\mu \) is an arbitrary bounded Radon measure \(\mu \) on \({\mathbb {R}}^n,\) we denote by \({{\widehat{\mu }}}\) the Fourier–Stieltjes transform of \(\mu \) and by \(\sigma \) the pure point part of \(\mu .\) A closed \(\varLambda \subset {{\mathbb {R}}}^n\) is a gregarious set if the following property is satisfied:

$$\begin{aligned} (\forall \mu )\, {{\widehat{\mu }}}=0\quad \mathrm{on}\, \varLambda \Rightarrow {{\widehat{\sigma }}}=0\, \mathrm{on}\,\varLambda . \end{aligned}$$

Gregarious sets are studied in this essay.

中文翻译：

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Radon测度的Fourier–Stieltjes变换的限制代数

如果\（\ mu \）是\（{\ mathbb {R}} ^ n，\）上的任意有界Radon度量\（\ mu \），我们用\（{{\ widehat {\ mu}}}} \ ）\（\ mu \ ）的傅里叶– Stieltjes变换，并通过\（\ mu。\的纯点部分）通过\（\ sigma \）进行封闭\（\ varLambda \ subset {{\ mathbb {R}}}如果满足以下属性，则^ n \）是一个合意的集合：

$$ \ begin {aligned}（\ forall \ mu）\，{{\ widehat {\ mu}}} = 0 \ quad \ mathrm {on} \，\ varLambda \ Rightarrow {{\ widehat {\ sigma}}} = 0 \，\ mathrm {on} \，\ varLambda。\ end {aligned} $$

本文研究了合群。