Real Analysis (Paperback)

Fon-Che Liu

  • 出版商: Oxford University
  • 出版日期: 2016-12-27
  • 售價: $2,670
  • 貴賓價: 9.5$2,537
  • 語言: 英文
  • 頁數: 288
  • 裝訂: Paperback
  • ISBN: 0198790430
  • ISBN-13: 9780198790433
  • 相關分類: 數值分析 Numerical-analysis
  • 立即出貨(限量) (庫存=2)

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<內容簡介>

 

Real Analysis is indispensable for in-depth understanding and effective application of methods of modern analysis. This concise and friendly book is written for early graduate students of mathematics or of related disciplines hoping to learn the basics of Real Analysis with reasonable ease. The essential role of Real Analysis in the construction of basic function spaces necessary for the application of Functional Analysis in many fields of scientific disciplines is demonstrated with due explanations and illuminating examples.

After the introductory chapter, a compact but precise treatment of general measure and integration is taken up so that readers have an overall view of the simple structure of the general theory before delving into special measures. The universality of the method of outer measure in the construction of measures is emphasized because it provides a unified way of looking for useful regularity properties of measures. The chapter on functions of real variables sits at the core of the book; it treats in detail properties of functions that are not only basic for understanding the general feature of functions but also relevant for the study of those function spaces which are important when application of functional analytical methods is in question. This is then followed naturally by an introductory chapter on basic principles of Functional Analysis which reveals, together with the last two chapters on the space of p-integrable functions and Fourier integral, the intimate interplay between Functional Analysis and Real Analysis. Applications of many of the topics discussed are included to motivate the readers for further related studies; these contain explorations towards probability theory and partial differential equations.

<章節目錄>

 

1: Introduction and Preliminaries
2: A Glimpse of Measure and Integration
3: Construction of Measures
4: Functions of Real Variables
5: Basic Principles of Linear Analysis
6: Lp Spaces
7: Fourier Integral and Sobolev Space Hs
8: Postscript

 

商品描述(中文翻譯)

內容簡介:

《實分析》對於深入理解和有效應用現代分析方法至關重要。這本簡潔友好的書籍是為數學或相關學科的初級研究生撰寫的,希望以相對輕松的方式學習實分析的基礎知識。書中詳細解釋並通過啟發性的例子展示了實分析在許多科學學科領域中構建基本函數空間的重要作用。

在介紹章節之後,書中簡潔而精確地介紹了一般測度和積分的處理,以便讀者在深入研究特殊測度之前對一般理論的簡單結構有整體的了解。強調了外測度方法在構建測度中的普遍性,因為它提供了一種統一的方式來尋找測度的有用規律性。實變數函數的章節是本書的核心;它詳細介紹了函數的性質,這些性質不僅對於理解函數的一般特徵至關重要,而且對於研究在應用函數分析方法時重要的函數空間也是相關的。接下來自然而然地是一個關於函數分析基本原理的介紹章節,它與關於p可積函數和傅立葉積分的最後兩章一起,展示了函數分析和實分析之間的緊密相互作用。書中包含了許多討論主題的應用,以激發讀者進一步進行相關研究;這些應用包括對概率論和偏微分方程的探索。

章節目錄:

1:引言和預備知識
2:測度和積分的一瞥
3:測度的構建
4:實變數函數
5:線性分析的基本原理
6:Lp空間
7:傅立葉積分和Sobolev空間Hs
8:附錄