G. Bennett and N.J. Kalton: "Consistency theorems for almost convergence." Trans. Amer. Math. Soc., 198:23--43, 1974.
J. Boos: "Classical and modern methods in summability." Oxford University Press, New York, 2000.
J. Connor and K.-G. Grosse-Erdmann: "Sequential definitions of continuity for real functions." Rocky Mt. J. Math., 33(1):93--121, 2003.
G.G. Lorentz: "A contribution to the theory of divergent sequences." Acta Math., 80:167--190, 1948.
Hardy, G. H., Divergent Series, Oxford: Clarendon Press, 1949.
行進 30, 2023
几乎收敛序列, 倘若有界实序列, displaystyle, 在每个巴拿赫极限下都得到同一个值l, displaystyle, displaystyle, 则称其为几乎收敛, 英語, almost, convergent, 到l, displaystyle, 洛仑兹证明了, 序列, displaystyle, 几乎收敛当且仅当, displaystyle, limits, infty, frac, ldots, 关于n, displaystyle, 一致成立, 上述极限具体可写为, displaystyle, fo. 倘若有界实序列 x n displaystyle x n 在每个巴拿赫极限下都得到同一个值L displaystyle L x n displaystyle x n 则称其为几乎收敛 英語 Almost convergent 到L displaystyle L 的 洛仑兹证明了 序列 x n displaystyle x n 几乎收敛当且仅当 lim p x n x n p 1 p L displaystyle lim limits p to infty frac x n ldots x n p 1 p L 关于n displaystyle n 一致成立 上述极限具体可写为 e gt 0 p 0 p gt p 0 n x n x n p 1 p L lt e displaystyle forall varepsilon gt 0 exists p 0 forall p gt p 0 forall n left frac x n ldots x n p 1 p L right lt varepsilon 几乎收敛的概念是可和性理论中的研究对象 它是不能表示为矩阵可和法的可和法 1 外部链接 编辑几乎收敛 PlanetMath 参考资料 编辑 Hardy p 52 G Bennett and N J Kalton Consistency theorems for almost convergence Trans Amer Math Soc 198 23 43 1974 J Boos Classical and modern methods in summability Oxford University Press New York 2000 J Connor and K G Grosse Erdmann Sequential definitions of continuity for real functions Rocky Mt J Math 33 1 93 121 2003 G G Lorentz A contribution to the theory of divergent sequences Acta Math 80 167 190 1948 Hardy G H Divergent Series Oxford Clarendon Press 1949 取自 https zh wikipedia org w index php title 几乎收敛序列 amp oldid 75951016, 维基百科，wiki，书籍，书籍，图书馆，
