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Introductory Real Analysis (Dover Books on Mathematics) First Edition
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The first four chapters present basic concepts and introductory principles in set theory, metric spaces, topological spaces, and linear spaces. The next two chapters consider linear functionals and linear operators, with detailed discussions of continuous linear functionals, the conjugate space, the weak topology and weak convergence, generalized functions, basic concepts of linear operators, inverse and adjoint operators, and completely continuous operators. The final four chapters cover measure, integration, differentiation, and more on integration. Special attention is here given to the Lebesque integral, Fubini's theorem, and the Stieltjes integral. Each individual section — there are 37 in all — is equipped with a problem set, making a total of some 350 problems, all carefully selected and matched.
With these problems and the clear exposition, this book is useful for self-study or for the classroom — it is basic one-year course in real analysis. Dr. Silverman is a former member of the Institute of Mathematical Sciences of New York University and the Lincoln Library of M.I.T. Along with his translation, he has revised the text with numerous pedagogical and mathematical improvements and restyled the language so that it is even more readable.
- ISBN-100486612260
- ISBN-13978-0486612263
- EditionFirst Edition
- PublisherDover Publications
- Publication dateJune 1, 1975
- LanguageEnglish
- Dimensions5.75 x 1 x 8.5 inches
- Print length416 pages
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Product details
- Publisher : Dover Publications; First Edition (June 1, 1975)
- Language : English
- Paperback : 416 pages
- ISBN-10 : 0486612260
- ISBN-13 : 978-0486612263
- Item Weight : 1.1 pounds
- Dimensions : 5.75 x 1 x 8.5 inches
- Best Sellers Rank: #456,519 in Books (See Top 100 in Books)
- #86 in Number Theory (Books)
- #361 in Calculus (Books)
- #512 in Algebra
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To give a concrete example: One reviewer has suggested that the theorem "Every infinite set has a countable subset" is proved without stating that the axiom of choice is required. This is certainly a serious lapse of rigour, BUT, in a later page, the author explains the axiom of choice (and several equivalent assertions) and also touches upon the fact that there are some very deep set theoretic questions, not yet fully resolved, concerning this axiom. He goes on to say "The axiom of choice will be assumed in this book. In fact, without it, we will be severely hampered for making various set-theoretic constructions". It is evident that the above theorem is one such construction.
This book emphasizes an intuitive approach to the subject, something which in my opinion is neglected by far too many books. Rigour is necessary but never sufficient to acheive proficiency in math!
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Los temas tratados y la variedad también constituyen una parte muy atractiva del libro.
Lo único que no me agradó fue la baja calidad de la impresión y del papel utilizado. Fuera de ello, un excelente libro.

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