Fundamentals of Real Analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1999
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Integration theory and general topology form the core of this textbook for a first-year graduate course in real analysis. After the foundational material in the first chapter (construction of the reals, cardinal and ordinal numbers, Zorn's lemma and transfinite induction), measure, integral and topology are introduced and developed as recurrent themes of increasing depth. The treatment of integration theory is quite complete (including the convergence theorems, product measure, absolute continuity, the Radon-Nikodym theorem, and Lebesgue's theory of differentiation and primitive functions), while topology, predominantly metric, plays a supporting role. In the later chapters, integral and topology coalesce in topics such as function spaces, the Riesz representation theorem, existence theorems for an ordinary differential equation, and integral operators with continuous kernel function. In particular, the material on function spaces lays a firm foundation for the study of functional analysis |
| Beschreibung: | 1 Online-Ressource (XI, 479 p.) 98 illus |
| ISBN: | 9781461205494 9780387984803 |
| ISSN: | 0172-5939 |
| DOI: | 10.1007/978-1-4612-0549-4 |
Internformat
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Datensatz im Suchindex
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| dewey-ones | 515 - Analysis |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-0549-4 |
| format | Electronic eBook |
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| spelling | Berberian, Sterling K. Verfasser aut Fundamentals of Real Analysis by Sterling K. Berberian New York, NY Springer New York 1999 1 Online-Ressource (XI, 479 p.) 98 illus txt rdacontent c rdamedia cr rdacarrier Universitext 0172-5939 Integration theory and general topology form the core of this textbook for a first-year graduate course in real analysis. After the foundational material in the first chapter (construction of the reals, cardinal and ordinal numbers, Zorn's lemma and transfinite induction), measure, integral and topology are introduced and developed as recurrent themes of increasing depth. The treatment of integration theory is quite complete (including the convergence theorems, product measure, absolute continuity, the Radon-Nikodym theorem, and Lebesgue's theory of differentiation and primitive functions), while topology, predominantly metric, plays a supporting role. In the later chapters, integral and topology coalesce in topics such as function spaces, the Riesz representation theorem, existence theorems for an ordinary differential equation, and integral operators with continuous kernel function. In particular, the material on function spaces lays a firm foundation for the study of functional analysis Mathematics Real Functions Mathematik Analysis (DE-588)4001865-9 gnd rswk-swf Reelle Analysis (DE-588)4627581-2 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Reelle Analysis (DE-588)4627581-2 s 2\p DE-604 Analysis (DE-588)4001865-9 s 3\p DE-604 https://doi.org/10.1007/978-1-4612-0549-4 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Berberian, Sterling K. Fundamentals of Real Analysis Mathematics Real Functions Mathematik Analysis (DE-588)4001865-9 gnd Reelle Analysis (DE-588)4627581-2 gnd |
| subject_GND | (DE-588)4001865-9 (DE-588)4627581-2 (DE-588)4123623-3 |
| title | Fundamentals of Real Analysis |
| title_auth | Fundamentals of Real Analysis |
| title_exact_search | Fundamentals of Real Analysis |
| title_full | Fundamentals of Real Analysis by Sterling K. Berberian |
| title_fullStr | Fundamentals of Real Analysis by Sterling K. Berberian |
| title_full_unstemmed | Fundamentals of Real Analysis by Sterling K. Berberian |
| title_short | Fundamentals of Real Analysis |
| title_sort | fundamentals of real analysis |
| topic | Mathematics Real Functions Mathematik Analysis (DE-588)4001865-9 gnd Reelle Analysis (DE-588)4627581-2 gnd |
| topic_facet | Mathematics Real Functions Mathematik Analysis Reelle Analysis Lehrbuch |
| url | https://doi.org/10.1007/978-1-4612-0549-4 |
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