| ON SOME INTEGRATION BY PARTS FORMULATE FOR THE ASP-INTEGRAL |
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| 引用本文： | XuDongfu LeeTuo-Yeong LeePeng-Yee. ON SOME INTEGRATION BY PARTS FORMULATE FOR THE ASP-INTEGRAL[J]. 数学研究, 1994, 27(1): 181-184 |
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| 作者姓名： | XuDongfu LeeTuo-Yeong LeePeng-Yee |
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| 作者单位： | [1]JimeiTeachersCollege,Xiarnen,361021 [2]DeptofMath,NationalUnivofSingapore,Singapore0511 [3]DeptofMat,h,NationalUnivofSignapore,Singapore0511 |
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| 摘 要： | The main results of this paper are as follows；Let F be approximately continuous on[a,b]and g be of bounded variation on[a,b]. Then (APS)∫^ba Fexists if and only if (APS)∫^ba gdf existe. Furthermore,suppose (APS)∫^ba Fdy or (APS)∫^ba gdF exists, then we have (APS)∫^ba Fdg (APS)∫^bagdf=F(b)g(b)-F(a)g(a)
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| 关 键 词： | 连续逼近 存在性 有界变量 AP积分 |
ON SOME INTEGRATION BY PARTS FORMULATE FOR THE ASP-INTEGRAL |
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| XuDongfu LeeTuo-Yeong LeePeng-Yee. ON SOME INTEGRATION BY PARTS FORMULATE FOR THE ASP-INTEGRAL[J]. Journal of Mathematical Study, 1994, 27(1): 181-184 |
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| Authors: | XuDongfu LeeTuo-Yeong LeePeng-Yee |
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| Affiliation: | [1]JimeiTeachersCollege,Xiarnen,361021 [2]DeptofMath,NationalUnivofSingapore,Singapore0511 [3]DeptofMat,h,NationalUnivofSignapore,Singapore0511 |
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| Abstract: | The main results of this paper are as follows:Let F be approximately continuous on [a,bl and g be of bounded variation on [a,b]. Then(APS) dg exists if and only if (APS)dF exists. Furthermore, suppose (APS)Fdy or(APS)dF exists,then we have(APS)Fdg (APS)gdF = F(b)g(b) -F(a)g(a) |
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| Keywords: | AFC on E APS-Integral |
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