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Essentials of Measure Theory

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Essentials of Measure Theory/ by Carlos S. Kubrusly.
作者:	Kubrusly, Carlos S.
面頁冊數:	XIII, 279 p. 1 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Measure theory. -
電子資源:	https://doi.org/10.1007/978-3-319-22506-7
ISBN:	9783319225067

Essentials of Measure Theory
Kubrusly, Carlos S.

Essentials of Measure Theory[electronic resource] /by Carlos S. Kubrusly. - 1st ed. 2015. - XIII, 279 p. 1 illus.online resource.

Preface -- Part I. Introduction to Measure and Integration.-1. Measurable Functions -- 2. Measure on a σ-Algebra -- 3. Integral of Nonnegative Functions -- 4. Integral of Real-Valued Functions -- 5. Banach Spaces Lp -- 6. Convergence of Functions -- 7. Decomposition of Measures -- 8. Extension of Measures -- 9. Product Measures -- Part II -- 10. Remarks on Integrals -- 11. Borel Measure -- 12. Representation Theorems -- 13. Invariant Measures -- References -- Index.

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:

527848
Measure theory.

LC Class. No.: QA312-312.5

Dewey Class. No.: 515.42

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