Bøker av Heinz Bauer

The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 35 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics.While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob. Titles in planning includeFlavia Smarazzo and Alberto Tesei, Measure Theory: Radon Measures, Young Measures, and Applications to Parabolic Problems (2019)Elena Cordero and Luigi Rodino, Time-Frequency Analysis of Operators (2019)Mark M. Meerschaert, Alla Sikorskii, and Mohsen Zayernouri, Stochastic and Computational Models for Fractional Calculus, second edition (2020)Mariusz Lemanczyk, Ergodic Theory: Spectral Theory, Joinings, and Their Applications (2020)Marco Abate, Holomorphic Dynamics on Hyperbolic Complex Manifolds (2021)Miroslava Antic, Joeri Van der Veken, and Luc Vrancken, Differential Geometry of Submanifolds: Submanifolds of Almost Complex Spaces and Almost Product Spaces (2021)Kai Liu, Ilpo Laine, and Lianzhong Yang, Complex Differential-Difference Equations (2021)Rajendra Vasant Gurjar, Kayo Masuda, and Masayoshi Miyanishi, Affine Space Fibrations (2022)

Heinz Bauer (1928-2002) was one of the prominent figures in Convex Analysis and Potential Theory in the second half of the 20th century. The Bauer minimum principle and Bauer's work on Silov's boundary and the Dirichlet problem are milestones in convex analysis. Axiomatic potential theory owes him what is known by now as Bauer harmonic spaces. These Selecta collect more than twenty of Bauer's research papers including his seminal papers in Convex Analysis and Potential Theory. Above his research contributions Bauer is best known for his art of writing survey articles. Five of his surveys on different topics are reprinted in this volume. Among them is the well-known article Approximation and Abstract Boundary, for which he was awarded with the Chauvenet Price by the American Mathematical Association in 1980.

The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 35 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics.While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob. Titles in planning includeFlavia Smarazzo and Alberto Tesei, Measure Theory: Radon Measures, Young Measures, and Applications to Parabolic Problems (2019)Elena Cordero and Luigi Rodino, Time-Frequency Analysis of Operators (2019)Mark M. Meerschaert, Alla Sikorskii, and Mohsen Zayernouri, Stochastic and Computational Models for Fractional Calculus, second edition (2020)Mariusz Lemanczyk, Ergodic Theory: Spectral Theory, Joinings, and Their Applications (2020)Marco Abate, Holomorphic Dynamics on Hyperbolic Complex Manifolds (2021)Miroslava Antic, Joeri Van der Veken, and Luc Vrancken, Differential Geometry of Submanifolds: Submanifolds of Almost Complex Spaces and Almost Product Spaces (2021)Kai Liu, Ilpo Laine, and Lianzhong Yang, Complex Differential-Difference Equations (2021)Rajendra Vasant Gurjar, Kayo Masuda, and Masayoshi Miyanishi, Affine Space Fibrations (2022)

Frontmatter -- Inhaltsverzeichnis -- Literatur -- Einleitung -- Bezeichnungen -- Erster Teil. Maß- und Integrationstheorie -- Zweiter Teil. Wahrscheinlichkeitstheorie -- Namen- und Sachverzeichnis -- Backmatter

Frontmatter -- Kapitel I Maßtheorie -- § 1. s-Algebren und ihre Erzeuger -- § 2. Dynkin-Systeme -- § 3. Inhalte, Prämaße, Maße -- § 4. Lebesguesches Prämaß -- § 5. Fortsetzung eines Prämaßes zu einem Maß -- § 6. Lebesgue-Borelsches Maß und Maße auf der Zahlengeraden -- § 7. Meßbare Abbildungen und Bildmaße -- § 8. Abbildungseigenschaften des Lebesgue-Borelschen Maßes -- Kapitel II Integrationstheorie -- § 9. Meßbare numerische Funktionen -- § 10. Elementarfunktionen und ihr Integral -- § 11. Das Integral nichtnegativer meßbarer Funktionen -- § 12. Integrierbarkeit -- § 13. Fast überall bestehende Eigenschaften -- § 14. Die Räume Lp (µ) -- § 15. Konvergenzsätze -- § 16. Anwendungen der Konvergenzsätze -- § 17. Maße mit Dichten - Satz von Radon-Nikodym -- § 18* Signierte Maße -- § 19. Integration bezüglich eines Bildmaßes -- § 20. Stochastische Konvergenz -- § 21. Gleichgradige Integrierbarkeit -- Kapitel III Produktmaße -- § 22. Produkte von s-Algebren und Maßen -- § 23. Produktmaße und Satz von Fubini -- §24. Faltung endlicher Borel-Maße -- Kapitel IV Maße auf topologischen Räumen -- § 25. Borelsche Mengen, Borel- und Radon-Maße -- § 26. Radon-Maße auf polnischen Räumen -- § 27. Eigenschaften lokal-kompakter Räume -- § 28. Konstruktion von Radon-Maßen auf lokal-kompakten Räumen -- § 29. Rieszscher Darstellungssatz -- § 30. Konvergenz von Radon-Maßen -- § 31. Vage Kompaktheit und Metrisierbarkeitsfragen -- Literaturverzeichnis -- Symbol-Verzeichnis -- Sach- und Namenverzeichnis