| 关于积分与极限交换充要条件的注 |
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| 引用本文： | 戚民驹.关于积分与极限交换充要条件的注[J].上海电机学院学报,2011,14(4):262-268. |
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| 作者姓名： | 戚民驹 |
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| 作者单位： | 上海电机学院数理教学部,上海,200240 |
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| 摘 要： | 分析了积分与极限交换的充要条件,引进了等度可积函数序列和几乎处处绝对连续函数序列概念。证明几乎处处收敛的可积函数列在极限函数未知是否可积的情况下,积分与极限交换的充要条件是函数列在S∞上积分等度收敛;证明可积函数列依测度收敛的情况下,积分与极限交换的充要条件是函数列在a,b]上积分等度收敛。
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| 关 键 词： | 等度可积函数序列 几乎处处收敛 依测度收敛 积分与极限交换 |
Necessary and Sufficient Condition of Commutation on Integral and Limit |
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| QI Minju.Necessary and Sufficient Condition of Commutation on Integral and Limit[J].JOurnal of Shanghai Dianji University,2011,14(4):262-268. |
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| Authors: | QI Minju |
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| Affiliation: | QI Minju(Department of Mathematics and Physics,Shanghai Dianji University,Shanghai 200240,China) |
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| Abstract: | The necessary and sufficient condition of the commutation on integral and limit is discussed. The concepts of equi-integrable function sequences and almost everywhere absolute continuous function sequences are introduced. The necessary and sufficient condition of commutation on integral and limit, in which the integrability of the limiting function is unknown, is proved. The necessary and sufficient condition of commutation on integral and limit, in which the integrable function sequence is convergent in measure, is proved. The conditions are that the function sequences are equi-convergent integral. |
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| Keywords: | equi-integrable {unction sequence almost everywhere convergence convergencein measure commutation on integral and limit |
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