| WEAK CONVERGENCE OF HENSTOCK INTEGRABLE SEQUENCES |
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| 作者姓名： | LuisaDiPiazza |
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| 作者单位： | DeptofMath,viaArchirafi3490123PalermoITALY |
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| 摘 要： | Some relationships between pointwise and weak convergence of a sequence of Henstock integrable functions are studied, In particular it is provided an example of a sequence of Henstock integrable functions whose pointwise limit is different from the weak one. By introducing an asymptotic version of the Henstock equiintegrability notion it is given a necessary and sufficient condition in order that a pointwisely convergent sequence of Henstock integrable functions is weakly convergent to its pointwise limit.
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| 关 键 词： | 亨斯托克积分 弱收敛 拓扑空间 H渐进积分序列 |
WEAK CONVERGENCE OF HENSTOCK INTEGRABLE SEQUENCES |
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| LuisaDiPiazza.WEAK CONVERGENCE OF HENSTOCK INTEGRABLE SEQUENCES[J].Journal of Mathematical Study,1994,27(1):148-153. |
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| Authors: | LuisaDiPiazza |
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| Institution: | DeptofMath,viaArchirafi3490123PalermoITALY |
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| Abstract: | Some relationships between pointwise and weak convergence of a sequenceof Henstock integrable functions are studied. In partiedar it is provided an example of a sequenceof Henstock integrable functions whose pointwise limit is different from the weak one.By introducing an asymptotic version of the Henstock equiintegrability notion it is given a necessary and sufficient condition in order that a pointwisely convergent sequence of Hfnstock tritegrable functions is weakly convergent to its pnintwise limit. |
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| Keywords: | Henstock integral Topology of the Denjoy-Henstock space Dual ofthe Denjoy-Henstock space Weak convergence Asymptotically H-integrable sequence |
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