This book covers the subject matter that is central to mathematical analysis: measure and integration theory, some point set topology, and rudiments of functional analysis. Also, a number of other topics are developed to illustrate the uses of this core material in important areas of mathematics and to introduce readers to more advanced techniques. Some of the material presented has never appeared outside of advanced monographs and research papers, or been readily available in comparative texts. About 460 exercises, at ...
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This book covers the subject matter that is central to mathematical analysis: measure and integration theory, some point set topology, and rudiments of functional analysis. Also, a number of other topics are developed to illustrate the uses of this core material in important areas of mathematics and to introduce readers to more advanced techniques. Some of the material presented has never appeared outside of advanced monographs and research papers, or been readily available in comparative texts. About 460 exercises, at varying levels of difficulty, give readers practice in working with the ideas presented here.
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Whatever the title may suggest, this is not a book for engineers looking for applications. If interested in analysis and the theory of integration, though, it is a good idea to give this a try.
The book is well structured and the prose clear. Yet it must be said that the style itself is also quite terse. This is a graduate textbook, and it says something about the style that the exercises are never questions or numerical problems. They are claims of the form "A, B implies C" which are to be proved by the student. This is not Kreyszig, so to speak.
