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Record Nr. |
UNINA9910826000403321 |
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Autore |
Folland G. B. |
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Titolo |
A guide to advanced real analysis / / Gerald B. Folland [[electronic resource]] |
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Pubbl/distr/stampa |
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Washington : , : Mathematical Association of America, , 2009 |
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ISBN |
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Descrizione fisica |
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1 online resource (x, 107 pages) : digital, PDF file(s) |
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Collana |
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Dolciani Mathematical Expositions, ; v. 37 |
Dolciani mathematical expositions ; ; no. 37 |
MAA guides ; ; no. 2 |
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Disciplina |
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Soggetti |
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Mathematical analysis |
Functions of real variables |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Title from publisher's bibliographic system (viewed on 02 Oct 2015). |
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Nota di bibliografia |
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Includes bibliographical references (p. 101-102) and index. |
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Nota di contenuto |
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Prologue: notation, terminology, and set theory -- Topology -- Measure and integration: general theory -- Measure and integration: constructions and special examples -- Rudiments of functional analysis -- Function spaces -- Topics in analysis on Euclidean Space. |
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Sommario/riassunto |
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A Guide to Advanced Real Analysis is an outline of the core material in the standard graduate-level real analysis course. It is intended as a resource for students in such a course as well as others who wish to learn or review the subject. On the abstract level, it covers the theory of measure and integration and the basics of point set topology, functional analysis, and the most important types of function spaces. On the more concrete level, it also deals with the applications of these general theories to analysis on Euclidean space: the Lebesgue integral, Hausdorff measure, convolutions, Fourier series and transforms, and distributions. The relevant definitions and major theorems are stated in detail. Proofs, however, are generally presented only as sketches, in such a way that the key ideas are explained but the technical details are omitted. In this way a large amount of material is presented in a concise and readable form. |
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