Measure, Integration And Function Spaces by Charles Swartz (PDF)

Description

This text contains a basic introduction to the abstract measure theory and the Lebesgue integral. Most of the standard topics in the measure and integration theory are discussed. In addition, topics on the Hewitt-Yosida decomposition, the Nikodym and Vitali-Hahn-Saks theorems and material on finitely additive set functions not contained in standard texts are explored. There is an introductory section on functional analysis, including the three basic principles, which is used to discuss many of the classic Banach spaces of functions and their duals. There is also a chapter on Hilbert space and the Fourier transform.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The book of Swartz goes about several subjects, divides in several chapters. The interesting parts for me were Measure Theory, Integration and the Functional Analysis.It is not a book to read on the Sunday afternoon, some graduate knowledge of themathematics is needed! The defintions, theorems and propostion are nice ordered andthe proofs are good to understand. Lebesgue integration is an important part ofthe book. Important are also the Additive Set Functions (finite and countable).It is interesting to note that in the whole book, there is no picture at all, onlytext. In the title of the book is mentioned Functions Spaces, may be some more attention could be spend to it then now is done.Using the book for a lecture? I should not do, it is more for self-study, with thehelp of an expert in the areas as mentioned above. It is good book for on the book-shelf and to search for interesting parts of Measure Theory.But looking in the book, searching for an answer on a question, will certainlygive rise to other questions. The books of I.K. Rana, An Introduction to Measureand Integration (sec.ed., GSM vol.45) or V.S. Pugachev, I. N. Sinitsyn: Lectures on Functional Analysis and Applications, are certainly worth to mention and then to use together with the book of Swartz,Blakske

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