資源描述：
《Real analysis.pdf》由會員上傳分享，免費在線閱讀，更多相關內(nèi)容在學術論文-天天文庫。
1、實變函數(shù)筆記cnyouwei@gmail.com?c2011-2012前言i前言獻給親愛的鐘老師.歡迎大家mailto:cnyouwei@gmail.com批評指正!持續(xù)更新，請關注http://iask.sina.com.cn/u/1776601564/ish.γ.ω.2012年5月于南京大學目錄前言i概論10.1連續(xù)函數(shù)的極限..........................10.2曲線長度..............................10.3微分與積分....................
2、.........20.4Riemann積分的局限性......................30.5Lebesgue積分與Lebesgue測度.................4第一章集合與點集61.1集合的運算.............................61.2映射與基數(shù).............................101.2.1映射.............................101.2.2特征函數(shù)與冪集......................111.2.3基數(shù).
3、............................131.3Rn中的點集............................201.3.1Rn中的度量........................201.3.2領域,內(nèi)點,開集,閉集...................211.3.3極限點,閉包........................231.3.4Cantor集..........................251.3.5閉集上連續(xù)函數(shù)的延拓定理...............301.4Bo
4、rel集與綱性定理........................34第二章Lebesgue可測集382.1環(huán)上的測度.............................382.1.1環(huán)Rn............................3802.1.2環(huán)Rn上的測度......................4202.2外測度................................482.3Lebesgue測度...........................532.4Lebesgue
5、可測集與Borel集的關系...............582.5Lebesgue測度的完備性問題...................622.5.1Lebesgue不可測集的存在性...............62ii目錄iii2.5.2測度的延拓.........................62第三章Lebesgue可測函數(shù)673.1Lebesgue可測函數(shù)的定義及其性質...............673.2Lebesgue可測函數(shù)的結構.....................693.3幾乎處處收斂與
6、依測度收斂...................753.3.1幾乎處處收斂........................753.3.2依測度收斂.........................783.4函數(shù)可測的充要條件及復合函數(shù)的可測性...........84第四章Lebesgue積分874.1測度有限集上非負可測函數(shù)的積分...............874.2一般可測集上一般可測函數(shù)的積分...............944.3Lebesgue積分的極限定理.....................1
7、064.4Lebesgue積分與連續(xù)函數(shù)之間的關系..............1164.5Fubini定理.............................118第五章測度導數(shù)與Newton-Lebniz公式1235.1Vitali覆蓋定理...........................1235.2Hahn分解定理...........................1285.3Radon測度的導數(shù).........................1335.4Radon-Nikodym定理.....
8、..................1405.5單調函數(shù)與有界變差函數(shù).....................1455.5.1單調函數(shù)..........................1455.5.2有界變差函數(shù)........................1495.6絕對連續(xù)函數(shù)............................157參考文獻162索引163
