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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Analysis Measure, Integration & Real Analysis
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Measure, Integration & Real Analysis
Sheldon Axler (Gebundene Ausgabe, Englisch)
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Beschreibung
This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Content is carefully curated to suit a single course, or two-semester sequence of courses, creating a versatile entry point for graduate studies in all… areas of pure and applied mathematics. Motivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the main ideas of the other approach. Lebesgue integration links into results such as the Lebesgue Differentiation Theorem. The development of products of abstract measures leads to Lebesgue measure on R n . Chapters on Banach spaces, L p spaces, and Hilbert spaces showcase major results such as the Hahn–Banach Theorem, Hölder’s Inequality, and the Riesz Representation Theorem. An in-depth study of linear maps on Hilbert spaces culminates in the Spectral Theorem and Singular Value Decomposition for compact operators, with an optional interlude in real and complex measures. Building on the Hilbert space material, a chapter on Fourier analysis provides an invaluable introduction to Fourier series and the Fourier transform. The final chapter offers a taste of probability. Extensively class tested at multiple universities and written by an award-winning mathematical expositor, Measure, Integration & Real Analysis is an ideal resource for students at the start of their journey into graduate mathematics. A prerequisite of elementary undergraduate real analysis is assumed; students and instructors looking to reinforce these ideas will appreciate the electronic Supplement for Measure, Integration & Real Analysis that is freely available online. For errata and updates, visit https://measure.axler.net/ Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
24.12.2019
Sprache
Englisch
EAN
9783030331429
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
Graduate Texts in Mathematics
Sonderedition
Nein
Autor
Sheldon Axler
Seitenanzahl
411
Auflage
1st edition 2020
Einbandart
Gebundene Ausgabe
Schlagwörter
Measure theory textbook, Graduate real analysis textbook, Open Access, Riemann integration, Lebesgue integration, Product measures, Signed and complex measures, Abstract measure, Lebesgue Differentiation Theorem, Banach spaces, Hilbert spaces, Hahn–Banach Theorem, Hölder’s Inequality, Riesz Representation Theorem, Spectral Theorem, Singular Value Decomposition, Fourier analysis, Fourier series, Fourier transform, Open Access math textbook
Thema-Inhalt
PBKL - Integralrechnung und -gleichungen
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer Nature Switzerland AG, Europaplatz 3,69115 Heidelberg, Germany, Heidelberg, Deutschland, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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