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Author | : Beloslav Riecan |
Publisher | : Springer |
Total Pages | : 0 |
Release | : 2010-12-03 |
Genre | : Mathematics |
ISBN | : 9789048148554 |
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The present book is a monograph including some recent results of mea sure and integration theory. It concerns three main ideas. The first idea deals with some ordering structures such as Riesz spaces and lattice or dered groups, and their relation to measure and integration theory. The second is the idea of fuzzy sets, quite new in general, and in measure theory particularly. The third area concerns some models of quantum mechanical systems. We study mainly models based on fuzzy set theory. Some recent results are systematically presented along with our suggestions for further development. The first chapter has an introductory character, where we present basic definitions and notations. Simultaneously, this chapter can be regarded as an elementary introduction to fuzzy set theory. Chapter 2 contains an original approach to the convergence of sequences of measurable functions. While the notion of a null set can be determined uniquely, the notion of a set of "small" measure has a fuzzy character. It is interesting that the notion of fuzzy set and the notion of a set of small measure (described mathematically by so-called small systems) were introduced independently at almost the same time. Although the axiomatic systems in both theories mentioned are quite different, we show that the notion of a small system can be considered from the point of view of fuzzy sets.
Author | : Beloslav Riecan |
Publisher | : Springer Science & Business Media |
Total Pages | : 389 |
Release | : 2013-06-29 |
Genre | : Mathematics |
ISBN | : 9401589194 |
Download Integral, Measure, and Ordering Book in PDF, ePub and Kindle
The present book is a monograph including some recent results of mea sure and integration theory. It concerns three main ideas. The first idea deals with some ordering structures such as Riesz spaces and lattice or dered groups, and their relation to measure and integration theory. The second is the idea of fuzzy sets, quite new in general, and in measure theory particularly. The third area concerns some models of quantum mechanical systems. We study mainly models based on fuzzy set theory. Some recent results are systematically presented along with our suggestions for further development. The first chapter has an introductory character, where we present basic definitions and notations. Simultaneously, this chapter can be regarded as an elementary introduction to fuzzy set theory. Chapter 2 contains an original approach to the convergence of sequences of measurable functions. While the notion of a null set can be determined uniquely, the notion of a set of "small" measure has a fuzzy character. It is interesting that the notion of fuzzy set and the notion of a set of small measure (described mathematically by so-called small systems) were introduced independently at almost the same time. Although the axiomatic systems in both theories mentioned are quite different, we show that the notion of a small system can be considered from the point of view of fuzzy sets.
Author | : Richard Wheeden |
Publisher | : CRC Press |
Total Pages | : 289 |
Release | : 1977-11-01 |
Genre | : Mathematics |
ISBN | : 1482229536 |
Download Measure and Integral Book in PDF, ePub and Kindle
This volume develops the classical theory of the Lebesgue integral and some of its applications. The integral is initially presented in the context of n-dimensional Euclidean space, following a thorough study of the concepts of outer measure and measure. A more general treatment of the integral, based on an axiomatic approach, is later given.
Author | : Richard L. Wheeden |
Publisher | : CRC Press |
Total Pages | : 524 |
Release | : 2015-04-24 |
Genre | : Mathematics |
ISBN | : 1498702902 |
Download Measure and Integral Book in PDF, ePub and Kindle
Now considered a classic text on the topic, Measure and Integral: An Introduction to Real Analysis provides an introduction to real analysis by first developing the theory of measure and integration in the simple setting of Euclidean space, and then presenting a more general treatment based on abstract notions characterized by axioms and with less
Author | : Beloslav Riecan |
Publisher | : Springer |
Total Pages | : 378 |
Release | : 2014-10-09 |
Genre | : Mathematics |
ISBN | : 9789401589208 |
Download Integral, Measure, and Ordering Book in PDF, ePub and Kindle
The present book is a monograph including some recent results of mea sure and integration theory. It concerns three main ideas. The first idea deals with some ordering structures such as Riesz spaces and lattice or dered groups, and their relation to measure and integration theory. The second is the idea of fuzzy sets, quite new in general, and in measure theory particularly. The third area concerns some models of quantum mechanical systems. We study mainly models based on fuzzy set theory. Some recent results are systematically presented along with our suggestions for further development. The first chapter has an introductory character, where we present basic definitions and notations. Simultaneously, this chapter can be regarded as an elementary introduction to fuzzy set theory. Chapter 2 contains an original approach to the convergence of sequences of measurable functions. While the notion of a null set can be determined uniquely, the notion of a set of "small" measure has a fuzzy character. It is interesting that the notion of fuzzy set and the notion of a set of small measure (described mathematically by so-called small systems) were introduced independently at almost the same time. Although the axiomatic systems in both theories mentioned are quite different, we show that the notion of a small system can be considered from the point of view of fuzzy sets.
Author | : G. E. Shilov |
Publisher | : Courier Corporation |
Total Pages | : 258 |
Release | : 2013-05-13 |
Genre | : Mathematics |
ISBN | : 0486165612 |
Download Integral, Measure and Derivative Book in PDF, ePub and Kindle
This treatment examines the general theory of the integral, Lebesque integral in n-space, the Riemann-Stieltjes integral, and more. "The exposition is fresh and sophisticated, and will engage the interest of accomplished mathematicians." — Sci-Tech Book News. 1966 edition.
Author | : Beloslav Riečan |
Publisher | : |
Total Pages | : 378 |
Release | : 1997 |
Genre | : Fuzzy sets |
ISBN | : 9788088683186 |
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This book is concerned with three main themes. The first deals with ordering structures such as Riesz spaces and lattice ordered groups and their relation to measure and integration theory. The second is the idea of fuzzy sets, which is quite new, particularly in measure theory. The third subject is the construction of models of quantum mechanical systems, mainly based on fuzzy sets. In this way some recent are systematically presented. This volume is suitable not only for specialists in measure and integration theory, ordered spaces, probability theory and ergodic theory, but also for students of theoretical and applied mathematics.
Author | : H. R. Pitt |
Publisher | : Courier Corporation |
Total Pages | : 130 |
Release | : 2012-01-01 |
Genre | : Mathematics |
ISBN | : 0486488152 |
Download Integration, Measure and Probability Book in PDF, ePub and Kindle
Introductory treatment develops the theory of integration in a general context, making it applicable to other branches of analysis. More specialized topics include convergence theorems and random sequences and functions. 1963 edition.
Author | : Sheldon Axler |
Publisher | : Springer Nature |
Total Pages | : 430 |
Release | : 2019-11-29 |
Genre | : Mathematics |
ISBN | : 3030331431 |
Download Measure, Integration & Real Analysis Book in PDF, ePub and Kindle
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 Rn. Chapters on Banach spaces, Lp 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/
Author | : Alan J. Weir |
Publisher | : CUP Archive |
Total Pages | : 316 |
Release | : 1974-11-14 |
Genre | : Mathematics |
ISBN | : 9780521204071 |
Download General Integration and Measure Book in PDF, ePub and Kindle
This is a sequel to Dr Weir's undergraduate textbook on Lebesgue Integration and Measure (CUP. 1973) in which he provided a concrete approach to the Lebesgue integral in terms of step functions and went on from there to deduce the abstract concept of Lebesgue measure. In this second volume, the treatment of the Lebesgue integral is generalised to give the Daniell integral and the related general theory of measure. This approach via integration of elementary functions is particularly well adapted to the proof of Riesz's famous theorems about linear functionals on the classical spaces C (X) and LP and also to the study of topological notions such as Borel measure. This book will be used for final year honours courses in pure mathematics and for graduate courses in functional analysis and measure theory.