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Essentials of measure theory[electronic resource] /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
杜威分類號:	515.42
書名/作者:	Essentials of measure theory/ by Carlos S. Kubrusly.
作者:	Kubrusly, Carlos S.
出版者:	Cham : : Springer International Publishing :, 2015.
面頁冊數:	xiii, 279 p. : : ill., digital ;; 24 cm.
Contained By:	Springer eBooks
標題:	Measure theory.
標題:	Topology.
標題:	Mathematics.
標題:	Measure and Integration.
ISBN:	9783319225067
ISBN:	9783319225050
摘要、提要註:	Classical in its approach, this textbook is thoughtfully designed and composed in two parts. Part I is meant for a one-semester beginning graduate course in measure theory, proposing an "abstract" approach to measure and integration, where the classical concrete cases of Lebesgue measure and Lebesgue integral are presented as an important particular case of general theory. Part II of the text is more advanced and is addressed to a more experienced reader. The material is designed to cover another one-semester graduate course subsequent to a first course, dealing with measure and integration in topological spaces. The final section of each chapter in Part I presents problems that are integral to each chapter, the majority of which consist of auxiliary results, extensions of the theory, examples, and counterexamples. Problems which are highly theoretical have accompanying hints. The last section of each chapter of Part II consists of Additional Propositions containing auxiliary and complementary results. The entire book contains collections of suggested readings at the end of each chapter in order to highlight alternate approaches, proofs, and routes toward additional results. With modest prerequisites, this text is intended to meet the needs of a contemporary course in measure theory for mathematics students and is also accessible to a wider student audience, namely those in statistics, economics, engineering, and physics. Part I may be also accessible to advanced undergraduates who fulfill the prerequisites which include an introductory course in analysis, linear algebra (Chapter 5 only), and elementary set theory.
電子資源:	http://dx.doi.org/10.1007/978-3-319-22506-7

Essentials of measure theory[electronic resource] /
Kubrusly, Carlos S.

Essentials of measure theory[electronic resource] /by Carlos S. Kubrusly. - Cham :Springer International Publishing :2015. - xiii, 279 p. :ill., digital ;24 cm.

Classical in its approach, this textbook is thoughtfully designed and composed in two parts. Part I is meant for a one-semester beginning graduate course in measure theory, proposing an "abstract" approach to measure and integration, where the classical concrete cases of Lebesgue measure and Lebesgue integral are presented as an important particular case of general theory. Part II of the text is more advanced and is addressed to a more experienced reader. The material is designed to cover another one-semester graduate course subsequent to a first course, dealing with measure and integration in topological spaces. The final section of each chapter in Part I presents problems that are integral to each chapter, the majority of which consist of auxiliary results, extensions of the theory, examples, and counterexamples. Problems which are highly theoretical have accompanying hints. The last section of each chapter of Part II consists of Additional Propositions containing auxiliary and complementary results. The entire book contains collections of suggested readings at the end of each chapter in order to highlight alternate approaches, proofs, and routes toward additional results. With modest prerequisites, this text is intended to meet the needs of a contemporary course in measure theory for mathematics students and is also accessible to a wider student audience, namely those in statistics, economics, engineering, and physics. Part I may be also accessible to advanced undergraduates who fulfill the prerequisites which include an introductory course in analysis, linear algebra (Chapter 5 only), and elementary set theory.

ISBN: 9783319225067

Standard No.: 10.1007/978-3-319-22506-7doiSubjects--Topical Terms:

495639
Measure theory.

LC Class. No.: QA312

Dewey Class. No.: 515.42

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