| 有限可加测度及其在Lebesgue内外测度上的应用 |
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| 引用本文： | 张敏,周仙耕.有限可加测度及其在Lebesgue内外测度上的应用[J].韶关学院学报,2010,31(9):6-9. |
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| 作者姓名： | 张敏 周仙耕 |
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| 作者单位： | 宁德师范学院数学系,福建宁德352100 |
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| 基金项目： | 宁德师范学院科研资助项目 |
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| 摘 要： | 证明了（Ω,Σ）上的任一有限可加测度μ可保变差的延拓为（Ω,2Ω）上一有限可加测度,满足‖‖=‖μ‖且｜Σ=μ.作为它的应用,可得到：m＊（s）=sμu∈pUμ（s）,m＊（s）=μi∈nfUμ（s）,其中U={μ∈F＋},μ为λ的保变差延拓,λ为（0,1],蒡）上的Lebesgue测度.
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| 关 键 词： | 有限可加测度 Banach空间 Lebesgue内（外）测度 |
Finitely additive measure and its application to Lebesgue inner(exterior) measure |
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| ZHANG Min,ZHOU Xian-geng.Finitely additive measure and its application to Lebesgue inner(exterior) measure[J].Journal of Shaoguan University(Social Science Edition),2010,31(9):6-9. |
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| Authors: | ZHANG Min ZHOU Xian-geng |
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| Institution: | (Department of Mathematics,Ningde Teachers College,Ningde 352100,Fujian,China) |
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| Abstract: | This paper shows that each finitely additive measures μ on（Ω,Σ） can be variation-persevered extension to finitely additive measure on（Ω,2Ω）,satisfying ‖‖=‖μ‖ and｜Σ=μ.As its application,it also proves that m＊（s）=sμu∈pU μ（s）,m＊（s）=iμn∈fU μ（s）,which U={μ∈F＋},μ is variation-persevered extended of λ andλ is Lebesgue measure on（0,1],Σ）. |
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| Keywords: | finitely additive measure Banach space Lebesgue inner（exterior）measure |
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