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小变形下弹性织物压力分布的建模与计算
  • ISSN号：1673-3851
  • 期刊名称：浙江理工大学学报
  • 时间：2013.9.9
  • 页码：677-684
  • 分类：O177[理学—数学;理学—基础数学]
  • 作者机构：[1]厦门大学数学科学学院,厦门361005
  • 相关基金：Supported partially by tile National Natural Science Foundation of China （11071201） Acknowledgements The author would like to thank Professor Lin Qun for his helpful conversations on this note.
  • 相关项目：纺织材料热湿传递数学模型与设计反问题的研究
作者： 蒋建益|徐定华|杨予|
关键词： LEBESGUE积分, LEBESGUE测度, 线性泛函, Lebesgue＇s integration, Lebesgue＇s mneasure, linear functional
中文摘要：

从泛函分析观点来看Lebesgue积分，使得Lebesgue积分可以用泛函分析最简单最基本的方法独立导出．基本做法是将Riemann对于区间[0，1]上的连续函数的积分看成连续函数空间C[0，1]上的连续线性泛函，再将它“自然”延拓到C[0，1]在积分范数意义下的完备化空间，而这个完备化空间正是Lebesgue可积函数空间L1[0，1]．

英文摘要：

This note is devoted to describe the classical Lebesgue integration from a functional point of view. Let C[0, 1] be the linear space of all real-valued continuous functions endowed with the norm ｜｜x｜｜ = f0^1 ｜x（t）｜dt and let X = C[0, 1] be its completion. We define a linear functional xR^＊ on C[0, 1] by {xR^＊, x） = fg x（t）dt in Riemann＇s sense, and let x＊ be the natural extension of xR^＊ from C[0, 1] to its completion C[0, 1]. With a sketch but self-contained proof, we show the Lebesgue integration is just the natural extension of xR^＊ to C[0, 1], that is, C[0, 1] = L1[0, 1] and （x＊, xI =- f0^1 x（t）dt in Lebesgue＇s sence.

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纺织材料热湿传递数学模型与设计反问题的研究
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期刊信息
  • 《浙江理工大学学报：社会科学版》
  • 主管单位:浙江省教育厅
  • 主办单位:浙江理工大学
  • 主编：陈文兴
  • 地址：杭州下沙高教园区（西区）
  • 邮编：310018
  • 邮箱：journal@zstu.edu.cn
  • 电话：0571-86843150 86843151 86843452
  • 国际标准刊号：ISSN：1673-3851
  • 国内统一刊号：ISSN：33-1338/TS
  • 邮发代号:
  • 获奖情况:
  • 全国中文核心期刊,全国高校自然科学优秀学报
  • 国内外数据库收录:
  • 中国国家哲学社会科学学术期刊数据库
  • 被引量:288