巴拿赫空间中Lebesgue性质研究

论文摘要

实值函数f在闭区间[a,b]上Riemann可积等价于f在[a,b]上几乎处处连续,但是这个性质并不能推广到所有Banach空间中.本文讨论向量值函数Riemann可积与几乎处处连续性之间的关系,若取值于某个Banach空间的每一个Riemann可积向量值函数都满足几乎处处连续,则称这个空间具有Lebesgue性质,因为Lebesgue首先证明R空间具有这个性质.哪些空间具备Lebesgue性质是本文首要探究的问题.第二章介绍向量值函数Riemann积分的定义与性质.并构造例子说明存在Rieman-n可积向量值函数不满足几乎处处连续,存在Riemann可积向量值函数不满足外有界变分,所以向量值函数Riemann可积与几乎处处连续之间的等价性不是在所有的Ba-nach空间中都称成立.第三章首先介绍Darboux可积的定义,映射f Darboux可积等价于几乎处处连续,向量值函数Darboux可积蕴涵其Riemann可积.这一部分主要探究l1,lp（1<p<∞）,l∞空间是否具有Lebesgue性质.我们在文献[2]中相关结论的基础上,证明l1（Γ）空间具有Lebesgue性质.

论文目录

文章来源

类型: 硕士论文

作者: 杨智纯

导师: 魏舟

关键词: 积分,向量值函数,空间,性质

来源: 云南大学

年度: 2019

分类: 基础科学

专业: 数学

单位: 云南大学

分类号: O177.2

总页数: 36

文件大小: 1189K

下载量: 12

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