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The Resource Basic Real Analysis, by Houshang H. Sohrab, (electronic resource)

Basic Real Analysis, by Houshang H. Sohrab, (electronic resource)

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Author
Contributor
Summary
This expanded second edition presents the fundamentals and touchstone results of real analysis in full rigor, but in a style that requires little prior familiarity with proofs or mathematical language. The text is a comprehensive and largely self-contained introduction to the theory of real-valued functions of a real variable. The chapters on Lebesgue measure and integral have been rewritten entirely and greatly improved. They now contain Lebesgue's differentiation theorem as well as his versions of the Fundamental Theorem(s) of Calculus. With expanded chapters, additional problems, and an expansive solutions manual, Basic Real Analysis, Second Edition, is ideal for senior undergraduates and first-year graduate students, both as a classroom text and a self-study guide. Reviews of first edition: The book is a clear and well-structured introduction to real analysis aimed at senior undergraduate and beginning graduate students. The prerequisites are few, but a certain mathematical sophistication is required. ... The text contains carefully worked out examples which contribute motivating and helping to understand the theory. There is also an excellent selection of exercises within the text and problem sections at the end of each chapter. In fact, this textbook can serve as a source of examples and exercises in real analysis. —Zentralblatt MATH The quality of the exposition is good: strong and complete versions of theorems are preferred, and the material is organised so that all the proofs are of easily manageable length; motivational comments are helpful, and there are plenty of illustrative examples. The reader is strongly encouraged to learn by doing: exercises are sprinkled liberally throughout the text and each chapter ends with a set of problems, about 650 in all, some of which are of considerable intrinsic interest. —Mathematical Reviews [This text] introduces upper-division undergraduate or first-year graduate students to real analysis.... Problems and exercises abound; an appendix constructs the reals as the Cauchy (sequential) completion of the rationals; references are copious and judiciously chosen; and a detailed index brings up the rear. —CHOICE Reviews--
Language
eng
Work
Publication
Edition
2nd ed. 2014.
Extent
XI, 683 pages : 3 illustrations ;
Contents
  • Preface
  • Set Theory
  • Sequences and Series of Real Numbers
  • Limits of Functions
  • Topology of R and Continuity
  • Metric Spaces
  • The Derivative
  • The Riemann Integral
  • Sequences and Series of Functions
  • Normed and Function Spaces
  • The Lebesgue Integral
  • Lebesgue Measure
  • General Measure and Probability
  • Appendix A: Construction of Real Numbers
  • References
  • Index
Isbn
9781493918416
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-1-4939-1841-6
Instance
Label
Basic Real Analysis
Title
Basic Real Analysis
Statement of responsibility
by Houshang H. Sohrab
Creator
Contributor
Author
Subject
Language
eng
Summary
This expanded second edition presents the fundamentals and touchstone results of real analysis in full rigor, but in a style that requires little prior familiarity with proofs or mathematical language. The text is a comprehensive and largely self-contained introduction to the theory of real-valued functions of a real variable. The chapters on Lebesgue measure and integral have been rewritten entirely and greatly improved. They now contain Lebesgue's differentiation theorem as well as his versions of the Fundamental Theorem(s) of Calculus. With expanded chapters, additional problems, and an expansive solutions manual, Basic Real Analysis, Second Edition, is ideal for senior undergraduates and first-year graduate students, both as a classroom text and a self-study guide. Reviews of first edition: The book is a clear and well-structured introduction to real analysis aimed at senior undergraduate and beginning graduate students. The prerequisites are few, but a certain mathematical sophistication is required. ... The text contains carefully worked out examples which contribute motivating and helping to understand the theory. There is also an excellent selection of exercises within the text and problem sections at the end of each chapter. In fact, this textbook can serve as a source of examples and exercises in real analysis. —Zentralblatt MATH The quality of the exposition is good: strong and complete versions of theorems are preferred, and the material is organised so that all the proofs are of easily manageable length; motivational comments are helpful, and there are plenty of illustrative examples. The reader is strongly encouraged to learn by doing: exercises are sprinkled liberally throughout the text and each chapter ends with a set of problems, about 650 in all, some of which are of considerable intrinsic interest. —Mathematical Reviews [This text] introduces upper-division undergraduate or first-year graduate students to real analysis.... Problems and exercises abound; an appendix constructs the reals as the Cauchy (sequential) completion of the rationals; references are copious and judiciously chosen; and a detailed index brings up the rear. —CHOICE Reviews--
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http://library.link/vocab/creatorName
Sohrab, Houshang H
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0
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
SpringerLink (Online service)
http://library.link/vocab/subjectName
  • Mathematics
  • Measure theory
  • Mathematical logic
Label
Basic Real Analysis, by Houshang H. Sohrab, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-1-4939-1841-6
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier.
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
Contents
Preface -- Set Theory -- Sequences and Series of Real Numbers -- Limits of Functions -- Topology of R and Continuity -- Metric Spaces -- The Derivative -- The Riemann Integral -- Sequences and Series of Functions -- Normed and Function Spaces -- The Lebesgue Integral -- Lebesgue Measure -- General Measure and Probability -- Appendix A: Construction of Real Numbers -- References -- Index
Control code
978-1-4939-1841-6
Dimensions
unknown
Edition
2nd ed. 2014.
Extent
XI, 683 pages : 3 illustrations ;
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9781493918416
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-1-4939-1841-6
Other physical details
1 online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1022051148
Label
Basic Real Analysis, by Houshang H. Sohrab, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-1-4939-1841-6
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier.
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
Contents
Preface -- Set Theory -- Sequences and Series of Real Numbers -- Limits of Functions -- Topology of R and Continuity -- Metric Spaces -- The Derivative -- The Riemann Integral -- Sequences and Series of Functions -- Normed and Function Spaces -- The Lebesgue Integral -- Lebesgue Measure -- General Measure and Probability -- Appendix A: Construction of Real Numbers -- References -- Index
Control code
978-1-4939-1841-6
Dimensions
unknown
Edition
2nd ed. 2014.
Extent
XI, 683 pages : 3 illustrations ;
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9781493918416
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-1-4939-1841-6
Other physical details
1 online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1022051148

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