Measure and Integration: An Introduction
暫譯: 測度與積分：入門指南
Mukhopadhyay, Satya N., Ray, Subhasis
- 出版商: Springer
- 出版日期: 2026-01-21
- 售價: $3,060
- 貴賓價: 9.5 折 $2,907
- 語言: 英文
- 頁數: 321
- 裝訂: Quality Paper - also called trade paper
- ISBN: 9819725135
- ISBN-13: 9789819725137
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相關分類:
工程數學 Engineering-mathematics
海外代購書籍(需單獨結帳)
商品描述
Designed for senior undergraduate and graduate students in mathematics, this textbook offers a comprehensive exploration of measure theory and integration. It acts as a pivotal link bridging the Riemann integral and the Lebesgue integral, with a primary focus on tracing the evolution of measure and integration from their historical roots. A distinctive feature of the book is meticulous guidance, providing a step-by-step journey through the subject matter, thus rendering complex concepts more accessible to beginners. A fundamental grasp of differential and integral calculus, as well as Riemann integration, is recommended to ensure a smoother comprehension of the material.
This textbook comprises 10 well-structured chapters, each thoughtfully organized to lead students from fundamental principles to advanced complexities. Beginning with the establishment of Lebesgue's measure on the real line and an introduction to measurable functions, the book then delves into exploring the cardinalities of various set classes. As readers progress, the subtleties of the Lebesgue integral emerge, showcasing its generalization of the Riemann integral and its unique characteristics in higher dimensions.
One of the book's distinctive aspects is its indepth comparison of the Lebesgue integral, improper Riemann integral, and Newton integral, shedding light on their distinct qualities and relative independence. Subsequent chapters delve into the realm of general measures, Lebesgue-Stieltje's measure, Hausdorff 's measure, and the concept of measure and integration in product spaces. Furthermore, the book delves into function spaces, such as �������� spaces, and navigates the intricacies of signed and complex measures, providing students with a comprehensive foundation in this vital area of mathematics.
商品描述(中文翻譯)
設計給數學的高年級本科生和研究生，這本教科書提供了對測度理論和積分的全面探索。它作為連接黎曼積分和勒貝格積分的關鍵橋樑，主要專注於追溯測度和積分的歷史根源。這本書的一個顯著特點是細緻的指導，提供逐步的學習過程，使複雜的概念對初學者更易於理解。建議具備微積分及黎曼積分的基本知識，以確保對材料的更順利理解。
這本教科書包含10個結構良好的章節，每個章節都經過深思熟慮的組織，旨在引導學生從基本原則到高級複雜性。書中首先建立了實數線上的勒貝格測度並介紹可測函數，然後深入探討各種集合類別的基數。隨著讀者的進步，勒貝格積分的微妙之處逐漸浮現，展示了其對黎曼積分的概括及其在高維度中的獨特特性。
這本書的一個獨特方面是對勒貝格積分、不當黎曼積分和牛頓積分的深入比較，闡明了它們的不同特質和相對獨立性。隨後的章節深入探討一般測度、勒貝格-斯蒂爾捷測度、豪斯多夫測度，以及在乘積空間中的測度和積分概念。此外，書中還探討了函數空間，如L^p空間，並深入研究有符號和複數測度的複雜性，為學生在這一數學重要領域提供了全面的基礎。
作者簡介
Satya N. Mukhopadhyay is Emeritus Professor at the Department of Mathematics, the University of Burdwan, West Bengal, India. A renowned mathematician, after earning his master's degree in Mathematics in 1962, he began teaching at the University of Burdwan in 1963. With over a remarkable 38 years, his passion for research led him to explore different types of derivatives and integrals, and how they connect to trigonometric series. In 1967, he earned his Ph.D. from the University of Calcutta. He was invited twice as Visiting Professor to the University of British Columbia in Canada, first in the early 1970s and then in the mid-1980s, during which he teamed up with Prof. P.S. Bullen for research. With more than 100 research papers to his credit, most of them appearing in international journals, he has reviewed more than 150 research papers for the Mathematical Reviews. Author of two books, Real Analysis and Higher-Order Derivatives, he has guided many students in achieving their Ph.D. degrees.
Subhasis Ray is Professor at the Department of Mathematics, Visva-Bharati University, West Bengal, India, since 2006. Earlier, he worked as Assistant Professor at Kalna College, affiliated with the University of Burdwan, West Bengal, from 2000-2006. A student of Prof. Satya N. Mukhopadhyay, Prof. Ray embarked on his mathematical journey and joined the University of Burdwan as a CSIR scholar in 1997, after completing his M.Sc. degree. He earned his Ph.D. in Mathematics under the supervision of Prof. Mukhopadhyay, in 2004.
His areas of interest are in real function theory, generalized derivatives on real lines, the theory of non-absolute integration, and its application to trigonometric series. Additionally, he has displayed a keen interest in soft set theory and fuzzy set theory. His prowess as a guide is evident from the Ph.D. students he has supervised, with five of them having been awarded doctorates and three others currently pursuing research under his guidance. Some of his notable works include "On Laplace derivative", "Soft set and soft group from the classical viewpoint", and "Soft measure theory". He also reviewed many research papers for the Mathematical Reviews.
作者簡介(中文翻譯)
Satya N. Mukhopadhyay 是印度西孟加拉邦布爾萬大學數學系的名譽教授。這位著名的數學家於1962年獲得數學碩士學位後，於1963年開始在布爾萬大學任教。在超過38年的教學生涯中，他對研究的熱情使他探索了不同類型的導數和積分，以及它們與三角級數的關聯。1967年，他在加爾各答大學獲得博士學位。他曾兩次受邀擔任加拿大不列顛哥倫比亞大學的訪問教授，第一次是在1970年代初，第二次是在1980年代中期，期間他與P.S. Bullen教授合作進行研究。他發表了超過100篇研究論文，大多數刊登在國際期刊上，並為《數學評論》審稿超過150篇研究論文。他是兩本書的作者，分別是《實分析》（Real Analysis）和《高階導數》（Higher-Order Derivatives），並指導了許多學生獲得博士學位。
Subhasis Ray 自2006年以來擔任印度西孟加拉邦維斯瓦-巴拉提大學數學系的教授。此前，他於2000年至2006年在布爾萬大學附屬的卡爾納學院擔任助理教授。作為Mukhopadhyay教授的學生，Ray教授於1997年在完成碩士學位後，作為CSIR獎學金獲得者加入布爾萬大學，開始他的數學之旅。他於2004年在Mukhopadhyay教授的指導下獲得數學博士學位。
他的研究興趣包括實函數理論、實線上的廣義導數、非絕對積分理論及其在三角級數中的應用。此外，他對軟集合理論和模糊集合理論也表現出濃厚的興趣。他作為指導者的能力在他所指導的博士生中得以體現，其中五位已獲得博士學位，另外三位目前在他的指導下進行研究。他的一些重要著作包括《拉普拉斯導數研究》（'On Laplace derivative'）、《從古典觀點看軟集合和軟群》（'Soft set and soft group from the classical viewpoint'）以及《軟測度理論》（'Soft measure theory'）。他也為《數學評論》審稿了許多研究論文。
