Spaces of Quasi-Measures

Canadian mathematical bulletin

关键词: Kloosterman sums;    oscillating coefficients;    estimate;   

DOI  :  10.4153/CMB-1999-035-5

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

We give a direct proof that the space of Baire quasi-measures on acompletely regular space (or the space of Borel quasi-measures on anormal space) is compact Hausdorff. We show that it is possible forthe space of Borel quasi-measures on a non-normal space to benon-compact. This result also provides an example of a Bairequasi-measure that has no extension to a Borel quasi-measure. Finally,we give a concise proof of the Wheeler-Shakmatov theorem, which statesthat if $X$ is normal and $dim(X) le 1$, then everyquasi-measure on $X$ extends to a measure.

【 授权许可】

Unknown