This text provides an introduction to the field of measure and integration theory. The first three chapters (Measure Theory, Integration Theory, Product Measures) basically follow the clear and approved exposition given in the author's earlier book on "Probability Theory and Measure Theory". Special emphasis is laid on a complete discussion of the transformation of measures and integration with respect to the product measure, convergence theorems, parameter depending integrals, as well as the Radon-Nikodym theorem. The final chapter, essentially new and written in a clear and concise style, deals with the theory of Radon measures on Polish or locally compact spaces. With the main results being Luzin's theorem, the Riesz representation theorem, the Portmanteau theorem, and a characterization of locally compact spaces which are Polish, this chapter is a true invitation to study topological measure theory. The text addresses graduate students, who wish to learn the fundamentals in measure and integration theory as needed in modern analysis and probability theory.
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"It is a pleasure to see Heinz Bauer's famous monograph Ma - und Intergrationstheorie [...] published in English. [...] The translation by Robert B. Burckel is careful and close to the German original. He has replaced references to German textbooks by references to English textbooks, and he has also added several interesting exercises, comments, and references. the typographical appearance of the book is excellent."Klaus D. Schmidt in: Zentralblatt Math, 10/2000 "Like the German original, the present textbook is a very readable and concise introduction to measure theory and integration.[...] In any case, it definitely is a valuable resource for both students and teachers."G. Teschl in: Internationale Mathematische Nachrichten, Wien, 189/2002
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Text: English (translation)
Original Language: German
Original Language: German
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First Sentence:
To geometrically simple subsets of the line, the plane, and 3-dimensional space, elementary geometry assigns "numerical measures" called length, area and volume. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
measurable numerical functions, vague topology, positive linear form, measurable real functions, vague convergence, stochastic convergence, stochastic limits, pairwise disjoint sets, normal representations, countable base, representing measure, locally compact space, measurable space, original topology, measure space, finite measure, density with respect Key Phrases - Capitalized Phrases (CAPs): (learn more)
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To geometrically simple subsets of the line, the plane, and 3-dimensional space, elementary geometry assigns "numerical measures" called length, area and volume. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
measurable numerical functions, vague topology, positive linear form, measurable real functions, vague convergence, stochastic convergence, stochastic limits, pairwise disjoint sets, normal representations, countable base, representing measure, locally compact space, measurable space, original topology, measure space, finite measure, density with respect Key Phrases - Capitalized Phrases (CAPs): (learn more)
Lebesgue Bored New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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This book cites 21
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12
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- Probability Theory (De Gruyter Studies in Mathematics) by Heinz Bauer in Front Matter (1), Front Matter (2), and Back Matter
- Nevanlinna Theory and Complex Differential Equations (De Gruyter Studies in Mathematics) by Ilpo Laine in Front Matter
- Gibbs Measures And Phase by Hans-Otto Georgii in Front Matter
- Riemannian Geometry (De Gruyter Studies in Mathematics) by Wilhelm P. A. Klingenberg in Front Matter
- Set Theory. Third Edition by Felix Hausdorff in Back Matter
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- Measures, Integrals and Martingales by René L. Schilling in Back Matter (1), and Back Matter (2)
- Knots (De Gruyter Studies in Mathematics, 5) by Gerhard Burde in Front Matter
- The Reidemeister Torsion of 3-Manifolds (De Gruyter Studies in Mathematics) by Liviu I. Nicolaescu in Front Matter
- Elliptic Curves: A Computational Approach (De Gruyter Studies in Mathematics) by Susanne Schmitt in Front Matter
- Stochastic Finance: An Introduction in Discrete Time (de Gruyter Studies in Mathematics) by Hans Follmer in Front Matter
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