Mcshane积分的LSRS收敛定理的新扩展  

New Extension of LSRS Convergence Theorem of Mcshane Integral

作　　者：李伟[1] 

机构地区：[1]集美大学理学院,福建厦门361021

出　　处：《集美大学学报（自然科学版）》2009年第2期195-197,共3页Journal of Jimei University：Natural Science

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.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.

关 键 词：MCSHANE积分 LEBESGUE积分 Vitali收敛定理 LSRS 

分 类 号：O171[理学—数学]