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Real Analysis
This textbook is designed for a year-long course in real analysis taken by beginning graduate and advanced undergraduate students in mathematics and other areas such as statistics, engineering, and economics. Written by one of the leading scholars in the field, it elegantly explores the core concept...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cham :
Springer International Publishing : Imprint: Birkhäuser,
2016.
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| Edición: | 1st ed. 2016. |
| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
| LEADER | 00000nam a22000005i 4500 | ||
|---|---|---|---|
| 001 | 978-3-319-30744-2 | ||
| 003 | DE-He213 | ||
| 005 | 20220118092552.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 160505s2016 sz | s |||| 0|eng d | ||
| 020 | |a 9783319307442 |9 978-3-319-30744-2 | ||
| 024 | 7 | |a 10.1007/978-3-319-30744-2 |2 doi | |
| 050 | 4 | |a QA331.5 | |
| 072 | 7 | |a PBKB |2 bicssc | |
| 072 | 7 | |a MAT034000 |2 bisacsh | |
| 072 | 7 | |a PBKB |2 thema | |
| 082 | 0 | 4 | |a 515.8 |2 23 |
| 100 | 1 | |a Loeb, Peter A. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Real Analysis |h [electronic resource] / |c by Peter A. Loeb. |
| 250 | |a 1st ed. 2016. | ||
| 264 | 1 | |a Cham : |b Springer International Publishing : |b Imprint: Birkhäuser, |c 2016. | |
| 300 | |a XII, 274 p. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 505 | 0 | |a Preface -- Set Theory and Numbers -- Measure on the Real Line -- Measurable Functions -- Integration -- Differentiation and Integration -- General Measure Spaces -- Introduction to Metric and Normed Spaces -- Hilbert Spaces -- Topological Spaces -- Measure Construction -- Banach Spaces -- Appendices -- References. . | |
| 520 | |a This textbook is designed for a year-long course in real analysis taken by beginning graduate and advanced undergraduate students in mathematics and other areas such as statistics, engineering, and economics. Written by one of the leading scholars in the field, it elegantly explores the core concepts in real analysis and introduces new, accessible methods for both students and instructors. The first half of the book develops both Lebesgue measure and, with essentially no additional work for the student, general Borel measures for the real line. Notation indicates when a result holds only for Lebesgue measure. Differentiation and absolute continuity are presented using a local maximal function, resulting in an exposition that is both simpler and more general than the traditional approach. The second half deals with general measures and functional analysis, including Hilbert spaces, Fourier series, and the Riesz representation theorem for positive linear functionals on continuous functions with compact support. To correctly discuss weak limits of measures, one needs the notion of a topological space rather than just a metric space, so general topology is introduced in terms of a base of neighborhoods at a point. The development of results then proceeds in parallel with results for metric spaces, where the base is generated by balls centered at a point. The text concludes with appendices on covering theorems for higher dimensions and a short introduction to nonstandard analysis including important applications to probability theory and mathematical economics. . | ||
| 650 | 0 | |a Functions of real variables. | |
| 650 | 0 | |a Functional analysis. | |
| 650 | 0 | |a Measure theory. | |
| 650 | 1 | 4 | |a Real Functions. |
| 650 | 2 | 4 | |a Functional Analysis. |
| 650 | 2 | 4 | |a Measure and Integration. |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783319307428 |
| 776 | 0 | 8 | |i Printed edition: |z 9783319307435 |
| 776 | 0 | 8 | |i Printed edition: |z 9783319808796 |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/978-3-319-30744-2 |z Texto Completo |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-SXMS | ||
| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||