Principles of Analysis: Measure, Integration, Functional Analysis, and Applications
暫譯: 分析學原理：測度、積分、泛函分析與應用
Junghenn, Hugo D.
相關主題
商品描述
Principles of Analysis: Measure, Integration, Functional Analysis, and Applications prepares readers for advanced courses in analysis, probability, harmonic analysis, and applied mathematics at the doctoral level. The book also helps them prepare for qualifying exams in real analysis. It is designed so that the reader or instructor may select topics suitable to their needs. The author presents the text in a clear and straightforward manner for the readers' benefit. At the same time, the text is a thorough and rigorous examination of the essentials of measure, integration and functional analysis.
The book includes a wide variety of detailed topics and serves as a valuable reference and as an efficient and streamlined examination of advanced real analysis. The text is divided into four distinct sections: Part I develops the general theory of Lebesgue integration; Part II is organized as a course in functional analysis; Part III discusses various advanced topics, building on material covered in the previous parts; Part IV includes two appendices with proofs of the change of the variable theorem and a joint continuity theorem. Additionally, the theory of metric spaces and of general topological spaces are covered in detail in a preliminary chapter .
Features:
- Contains direct and concise proofs with attention to detail
- Features a substantial variety of interesting and nontrivial examples
- Includes nearly 700 exercises ranging from routine to challenging with hints for the more difficult exercises
- Provides an eclectic set of special topics and applications
About the Author:
Hugo D. Junghenn is a professor of mathematics at The George Washington University. He has published numerous journal articles and is the author of several books, including Option Valuation: A First Course in Financial Mathematics and A Course in Real Analysis. His research interests include functional analysis, semigroups, and probability.
商品描述(中文翻譯)
《分析學原理：測度、積分、泛函分析與應用》
《分析學原理：測度、積分、泛函分析與應用》旨在協助讀者準備博士班程度的分析學、機率論、調和分析與應用數學進階課程。本書也能幫助讀者準備實分析（real analysis）資格考。全書的設計相當彈性，讀者或授課教師可以依照需求選擇適合的主題。作者以清晰直接的方式呈現內容，以便讀者理解；同時，本書也對測度、積分與泛函分析的基本要點進行全面且嚴謹的探討。
本書涵蓋各式各樣的詳細主題，既是相當有價值的參考書，也以有效且精簡的方式檢視進階實分析。全書分為四個部分：第一部建立 Lebesgue 積分的一般理論；第二部以泛函分析課程的形式編排；第三部在前兩部所介紹的內容之上，討論各種進階主題；第四部則包含兩篇附錄，分別提供變數變換定理與聯合連續性定理的證明。此外，導論章節也詳細介紹度量空間（metric spaces）與一般拓撲空間（general topological spaces）的理論。
特色：
• 提供直接、精簡且注重細節的證明
• 收錄大量有趣且具實質挑戰性的範例
• 包含近 700 題習題，難度從例行練習到高難度題目不等，並為較困難的習題提供提示
• 提供多元且內容豐富的專題與應用
作者簡介：
Hugo D. Junghenn 是 The George Washington University 的數學教授。他已發表許多期刊論文，並著有數本書籍，包括《Option Valuation: A First Course in Financial Mathematics》與《A Course in Real Analysis》。他的研究興趣包括泛函分析、半群與機率論。
作者簡介
Hugo D. Junghenn is a professor of mathematics at The George Washington University. He has published numerous journal articles and is the author of several books, including Option Valuation: A First Course in Financial Mathematics and A Course in Real Analysis. His research interests include functional analysis, semigroups, and probability.
作者簡介(中文翻譯)
Hugo D. Junghenn 是 The George Washington University 的數學教授。他發表了許多期刊論文，並著有數本書籍，包括《Option Valuation: A First Course in Financial Mathematics》和《A Course in Real Analysis》。他的研究興趣包括泛函分析、半群與機率論。
