Principles of Analysis 1st Edition

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1. ISBN-10

   1498773281
2. ISBN-13

   978-1498773287

Principles of Analysis: Measure, Integration, Beneficial Analysis, and Functions is a resource to prepare individuals for advanced programs in analysis, probability, harmonic analysis, and applied mathematics at the doctoral level. The book also aids in readiness for qualifying exams in real analysis. It is structured to allow readers or instructors to select appropriate problems based on their needs. The author delivers the content in a straightforward and approachable manner for the benefit of the readers. Concurrently, the content provides a comprehensive and rigorous exploration of the principles of measure, integration, and functional analysis.

The book encompasses a wide range of detailed problems and serves as a valuable reference and an efficient and concise exploration of advanced real analysis. The content is divided into four distinct sections: Part I establishes the general theory of Lebesgue integration; Part II is outlined as a course in functional analysis; Part III delves into various advanced topics, building upon materials covered in the preceding sections; Part IV includes two appendices with proofs of the change of the variable theorem and a joint continuity theorem. Furthermore, the theory of metric spaces and of fundamental topological spaces is extensively covered in an initial chapter.