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      首頁 > 測度論與概率論基礎
        測度論與概率論基礎
        叢書名: 北京大學數學教學系列叢書
      • 出版社: 北京大學出版社
      • 作者:程士宏
      • 譯者:
      • ISBN:9787301063453
      • 出版時間:2014年 4月
      • 獲獎:北京市高等教育精品教材建設立項項目
      • 價格: ¥15.00
      • 基本信息
        • 叢書名: 北京大學數學教學系列叢書
        • 開本: A5
        • 頁碼: 256
        • 版次: 1版
        • 上架時間: 2016-11-22 04:39:54
        • 教材類別: 數學
        • 適用分級: 研究生、本科
        • 適用專業: 概率統計、數學
        • 是否包銷: 否
      • 內容簡介
            書籍    數學書籍《測度論與概率論基礎》為高等院校概率統計系本科生“測度論與概率論基礎”課程的教材。測度論內容旨在“短平快”地為初等概率論與公理化的概率論之間搭起一座橋梁。本書通過精選在抽象分析中為建立概率論公理化系統所必需的測度論內容,在此基礎上,著重講述那些在初等概率中沒有解釋清楚或不可能解釋清楚的概念和公式。全書共分六章,內容包括:可測空間和可測函數、測度空間、積分、符號測度、乘積空間、獨立隨機變量序列等。本書選材少而精,敘述由淺入深,通俗易懂,難點分散,論證嚴謹。為了滿足非數學專業出身而又必須學習公理化概率論的讀者的需要,本書對于概念的解釋和定理的證明都盡量做得精細,使之便于自學。每章配有適量習題,書末給出大部分習題的解答或提示。《測度論與概率論基礎》可作為綜合性大學、理工科大學和高等師范院校數學系、概率統計系本科生和研究生的教材,也可作為從事經濟學和金融學的研究生和科技工作者的參考書。本書是大學生學習“高等概率論”、“高等統計學”和“隨機過程”等課程之前的必修內容。
      • 目 錄
        《測度論與概率論基礎》
        第一章可測空間和可測映射
        1集合及其運算
        2集合系
        3σ域的生成
        4可測映射和可測函數
        5可測函數的運算
        習題1
        第二章測度空間
        1測度的定義及性質
        2外測度
        3測度的擴張
        4測度空間的完全化
        5可測函數的收斂性
        習題2
        第三章積分
        1積分的定義
        2積分的性質
        3空間Lp(X,,μ)
        4概率空間的積分
        習題3
        第四章符號測度
        1符號測度
        2Hahn分解和Jordan分解
        3Radon-Nikodym定理
        4Lebesgue分解
        5條件期望和條件概率
        習題4
        第五章乘積空間
        1有限維乘積空間
        2多維Lebesgue-Stieltjes測度
        3可列維乘積空間的概率測度
        4任意無窮維乘積空間的概率測度
        習題5
        第六章獨立隨機變量序列
        1零一律和三級數定理
        2強大數律
        3特征函數
        4弱大數律
        5中心極限定理
        習題6
        附錄習題解答與提示
        名詞索引
        符號索引

      • 插 圖
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