几乎收敛序列
倘若有界实序列在每个巴拿赫极限下都得到同一个值,则称其为几乎收敛(英语:Almost convergent)到的。
洛仑兹证明了,序列几乎收敛当且仅当
关于一致成立。
上述极限具体可写为
外部链接
- 几乎收敛. PlanetMath.
参考资料
- ^ 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.