| Mcshane积分的LSRS收敛定理的新扩展 |
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| 引用本文： | 李伟. Mcshane积分的LSRS收敛定理的新扩展[J]. 集美大学学报(自然科学版), 2009, 14(2) |
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| 作者姓名： | 李伟 |
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| 作者单位： | 集美大学理学院,福建,厦门,361021 |
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| 摘 要： | 在Mcshane积分的LSRS收敛定理中建立了M-积分的LSRS收敛定理,并证明了该定理的条件比Lebesgue积分的控制收敛定理条件弱.本文首先证明一个引理,进一步证明了定理1,由此阐述了Mcshane积分的LSRS收敛定理中的定理比Lebesgue积分中Vitali收敛定理条件更弱,从而使Vitali定理成为LSRS定理的推论.
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| 关 键 词： | Mcshane积分 Lebesgue积分 Vitali收敛定理 |
New Extension of LSRS Convergence Theorem of Mcshane Integral |
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| LI Wei. New Extension of LSRS Convergence Theorem of Mcshane Integral[J]. the Editorial Board of Jimei University(Natural Science), 2009, 14(2) |
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| Authors: | LI Wei |
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| Affiliation: | School of Sciences;Jimei University;Xiamen 361021;China |
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| Abstract: | On the basis of LSRS convergence theorem of Mcshane integral,LSRS convergence theorem of M-integral was proved.It was found that the conditions of the theorem were much weaker than those of control convergence theorem in Lebesgue integral.First,lemma was proved,then theorem 1 was proved,and so that Vitali theorem became a corollary of LSRS theorem. |
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| Keywords: | LSRS |
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