Real Analysis : : Measure and Integration / / Marat V. Markin.
The philosophy of the book, which makes it quite distinct from many existing texts on the subject, is based on treating the concepts of measure and integration starting with the most general abstract setting and then introducing and studying the Lebesgue measure and integration on the real line as a...
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Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2019] ©2019 |
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Markin, Marat V., author. aut http://id.loc.gov/vocabulary/relators/aut Real Analysis : Measure and Integration / Marat V. Markin. Berlin ; Boston : De Gruyter, [2019] ©2019 1 online resource (XV, 339 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda De Gruyter Textbook Frontmatter -- Preface -- Acknowledgments -- Contents -- 1. Preliminaries -- 2. Basic Set Classes -- 3. Measures -- 4. Extension of Measures -- 5. Measurable Functions -- 6. Abstract Lebesgue Integral -- 7. Lp Spaces -- 8. Differentiation and Integration -- 9. Signed Measures -- A. The Axiom of Choice and Equivalents -- Bibliography -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star The philosophy of the book, which makes it quite distinct from many existing texts on the subject, is based on treating the concepts of measure and integration starting with the most general abstract setting and then introducing and studying the Lebesgue measure and integration on the real line as an important particular case. The book consists of nine chapters and appendix, with the material flowing from the basic set classes, through measures, outer measures and the general procedure of measure extension, through measurable functions and various types of convergence of sequences of such based on the idea of measure, to the fundamentals of the abstract Lebesgue integration, the basic limit theorems, and the comparison of the Lebesgue and Riemann integrals. Also, studied are Lp spaces, the basics of normed vector spaces, and signed measures. The novel approach based on the Lebesgue measure and integration theory is applied to develop a better understanding of differentiation and extend the classical total change formula linking differentiation with integration to a substantially wider class of functions. Being designed as a text to be used in a classroom, the book constantly calls for the student's actively mastering the knowledge of the subject matter. There are problems at the end of each chapter, starting with Chapter 2 and totaling at 125. Many important statements are given as problems and frequently referred to in the main body. There are also 358 Exercises throughout the text, including Chapter 1 and the Appendix, which require of the student to prove or verify a statement or an example, fill in certain details in a proof, or provide an intermediate step or a counterexample. They are also an inherent part of the material. More difficult problems are marked with an asterisk, many problems and exercises are supplied with "existential'' hints. The book is generous on Examples and contains numerous Remarks accompanying definitions, examples, and statements to discuss certain subtleties, raise questions on whether the converse assertions are true, whenever appropriate, or whether the conditions are essential. With plenty of examples, problems, and exercises, this well-designed text is ideal for a one-semester Master's level graduate course on real analysis with emphasis on the measure and integration theory for students majoring in mathematics, physics, computer science, and engineering. A concise but profound and detailed presentation of the basics of real analysis with emphasis on the measure and integration theory. Designed for a one-semester graduate course, with plethora of examples, problems, and exercises. Is of interest to students and instructors in mathematics, physics, computer science, and engineering. Prepares the students for more advanced courses in functional analysis and operator theory. ContentsPreliminariesBasic Set ClassesMeasuresExtension of MeasuresMeasurable FunctionsAbstract Lebesgue IntegralLp SpacesDifferentiation and IntegrationSigned MeasuresThe Axiom of Choice and Equivalents Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 30. Aug 2021) Lebesgue-Integral. Lp-Raum. Maßtheorie. Messbare Funktion. Reelle Analysis. MATHEMATICS / Functional Analysis. bisacsh Title is part of eBook package: De Gruyter DG Plus eBook-Package 2019 9783110719567 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE DG 2019 English 9783110616859 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2019 English 9783110610765 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2019 9783110664232 ZDB-23-DGG Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2019 English 9783110610406 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2019 9783110606362 ZDB-23-DMA EPUB 9783110598827 print 9783110600971 https://doi.org/10.1515/9783110600995 https://www.degruyter.com/isbn/9783110600995 Cover https://www.degruyter.com/cover/covers/9783110600995.jpg |
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English |
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Markin, Marat V., Markin, Marat V., |
spellingShingle |
Markin, Marat V., Markin, Marat V., Real Analysis : Measure and Integration / De Gruyter Textbook Frontmatter -- Preface -- Acknowledgments -- Contents -- 1. Preliminaries -- 2. Basic Set Classes -- 3. Measures -- 4. Extension of Measures -- 5. Measurable Functions -- 6. Abstract Lebesgue Integral -- 7. Lp Spaces -- 8. Differentiation and Integration -- 9. Signed Measures -- A. The Axiom of Choice and Equivalents -- Bibliography -- Index |
author_facet |
Markin, Marat V., Markin, Marat V., |
author_variant |
m v m mv mvm m v m mv mvm |
author_role |
VerfasserIn VerfasserIn |
author_sort |
Markin, Marat V., |
title |
Real Analysis : Measure and Integration / |
title_sub |
Measure and Integration / |
title_full |
Real Analysis : Measure and Integration / Marat V. Markin. |
title_fullStr |
Real Analysis : Measure and Integration / Marat V. Markin. |
title_full_unstemmed |
Real Analysis : Measure and Integration / Marat V. Markin. |
title_auth |
Real Analysis : Measure and Integration / |
title_alt |
Frontmatter -- Preface -- Acknowledgments -- Contents -- 1. Preliminaries -- 2. Basic Set Classes -- 3. Measures -- 4. Extension of Measures -- 5. Measurable Functions -- 6. Abstract Lebesgue Integral -- 7. Lp Spaces -- 8. Differentiation and Integration -- 9. Signed Measures -- A. The Axiom of Choice and Equivalents -- Bibliography -- Index |
title_new |
Real Analysis : |
title_sort |
real analysis : measure and integration / |
series |
De Gruyter Textbook |
series2 |
De Gruyter Textbook |
publisher |
De Gruyter, |
publishDate |
2019 |
physical |
1 online resource (XV, 339 p.) |
contents |
Frontmatter -- Preface -- Acknowledgments -- Contents -- 1. Preliminaries -- 2. Basic Set Classes -- 3. Measures -- 4. Extension of Measures -- 5. Measurable Functions -- 6. Abstract Lebesgue Integral -- 7. Lp Spaces -- 8. Differentiation and Integration -- 9. Signed Measures -- A. The Axiom of Choice and Equivalents -- Bibliography -- Index |
isbn |
9783110600995 9783110719567 9783110616859 9783110610765 9783110664232 9783110610406 9783110606362 9783110598827 9783110600971 |
url |
https://doi.org/10.1515/9783110600995 https://www.degruyter.com/isbn/9783110600995 https://www.degruyter.com/cover/covers/9783110600995.jpg |
illustrated |
Not Illustrated |
doi_str_mv |
10.1515/9783110600995 |
oclc_num |
1104713475 |
work_keys_str_mv |
AT markinmaratv realanalysismeasureandintegration |
status_str |
n |
ids_txt_mv |
(DE-B1597)494860 (OCoLC)1104713475 |
carrierType_str_mv |
cr |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter DG Plus eBook-Package 2019 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE DG 2019 English Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2019 English Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2019 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2019 English Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2019 |
is_hierarchy_title |
Real Analysis : Measure and Integration / |
container_title |
Title is part of eBook package: De Gruyter DG Plus eBook-Package 2019 |
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1806144477366059008 |
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