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MARC 21

Essentials of Measure Theory
Tag	Description
020	$a9783319225067
082	$a515.42
099	$aOnline resource: Springer
100	$aKubrusly, Carlos S.$d1947-
245	$aEssentials of Measure Theory$h[EBook]$cby Carlos S. Kubrusly.
250	$a1st ed. 2015.
260	$aCham$bSpringer International Publishing$c2015.
300	$aXIII, 279 p. 1 illus.$bonline resource.
336	$atext
338	$aonline resource
505	$aPreface -- 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.
520	$aClassical 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.
538	$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
710	$aSpringerLink (Online service)
856	$uhttp://dx.doi.org/10.1007/978-3-319-22506-7