Real Analysis: An Introduction To The Theory Of Real Functions And Integration

Real Analysis: An Introduction To The Theory Of Real Functions And Integration

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Designed For Use In A Twosemester Course On Abstract Analysis, Real Analysis: An Introduction To The Theory Of Real Functions And Integration Illuminates The Principle Topics That Constitute Real Analysis. Selfcontained, With Coverage Of Topology, Measure Theory, And Integration, It Offers A Thorough Elaboration Of Major Theorems, Notions, And Constructions Needed Not Only By Mathematics Students But Also By Students Of Statistics And Probability, Operations Research, Physics, And Engineering.Structured Logically And Flexibly Through The Author'S Many Years Of Teaching Experience, The Material Is Presented In Three Main Sections:Part 1, Chapters 1Through 3, Covers The Preliminaries Of Set Theory And The Fundamentals Of Metric Spaces And Topology. This Section Can Also Serves As A Text For First Courses In Topology.Part Ii, Chapter 4 Through 7, Details The Basics Of Measure And Integration And Stands Independently For Use In A Separate Measure Theory Course.Part Iii Addresses More Advanced Topics, Including Elaborated And Abstract Versions Of Measure And Integration Along With Their Applications To Functional Analysis, Probability Theory, And Conventional Analysis On The Real Line.Analysis Lies At The Core Of All Mathematical Disciplines, And As Such, Students Need And Deserve A Careful, Rigorous Presentation Of The Material. Real Analysis: An Introduction To The Theory Of Real Functions And Integration Offers The Perfect Vehicle For Building The Foundation Students Need For More Advanced Studies.

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Frequently Asked Questions

  • Q: What topics are covered in 'Real Analysis: An Introduction to the Theory of Real Functions and Integration'? A: The book covers essential topics in real analysis including set theory, metric spaces, topology, measure theory, and integration, structured into three main parts for comprehensive learning.
  • Q: Who is the author of this book? A: The author of the book is Jewgeni H. Dshalalow.
  • Q: What is the target audience for this book? A: This book is designed for mathematics students as well as those studying statistics, probability, operations research, physics, and engineering.
  • Q: Is this book suitable for beginners in analysis? A: Yes, the book is self-contained and provides a rigorous introduction, making it suitable for beginners and those looking to deepen their understanding of real analysis.
  • Q: What is the format of the book? A: The book is available in a hardcover format and consists of 584 pages.
  • Q: Does this book include exercises or problems for practice? A: While the description does not specify, many textbooks in analysis typically include exercises or problems; it is advisable to check the book for specific features.
  • Q: What is the publication date of this book? A: The book was published on September 28, 2000.
  • Q: Are there any prerequisites for studying this book? A: A basic understanding of calculus and linear algebra is often recommended as a prerequisite for studying real analysis.
  • Q: How is the content structured in this book? A: The content is structured into three main parts: preliminaries of set theory and topology, basics of measure and integration, and advanced topics related to functional analysis and probability.
  • Q: Can this book be used for self-study? A: Yes, the logical structure and comprehensive explanations make it suitable for self-study, although prior knowledge in mathematics is beneficial.