The book includes a wide variety of detailed topics and serves as a valuable reference and as an efficient and streamlined examination of advanced real analysis. The text is divided into four distinct sections: Part I develops the general theory of Lebesgue integration; Part II is organized as a course in functional analysis; Part III discusses various advanced topics, building on material covered in the previous parts; Part IV includes two appendices with proofs of the change of the variable theorem and a joint continuity theorem. Additionally, the theory of metric spaces and of general topological spaces are covered in detail in a preliminary chapter .

Features:

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• Contains direct and concise proofs with attention to detail
  
  
  
  
• Features a substantial variety of interesting and nontrivial examples
  
  
  
  
• Includes nearly 700 exercises ranging from routine to challenging with hints for the more difficult exercises
  
  
  
  
• Provides an eclectic set of special topics and applications
  
  

About the Author:

Hugo D. Junghenn is a professor of mathematics at The George Washington University. He has published numerous journal articles and is the author of several books, including Option Valuation: A First Course in Financial Mathematics and A Course in Real Analysis. His research interests include functional analysis, semigroups, and probability.