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Theories Of Integrationby Douglas S. Kurtz; Charles W. Swartz
World Scientific 2004; US$ 72.80This book presents a historical development of the integration theories of Riemann, Lebesgue, Henstock?Kurzweil, and McShane, showing how new theories of integration were developed to solve problems that earlier theories could not handle. It develops the basic properties of each integral in detail and provides comparisons of the different integrals. more...
Measure Theory and Filteringby Lakhdar Aggoun; Robert J. Elliott
Cambridge University Press 2004; US$ 88.00Provides an accessible introduction to measure theory and stochastic calculus, and develops into an excellent users' guide to filtering. A complete resource for engineers, or anyone with an interest in implementation of filtering techniques. Three chapters concentrate on applications from finance, genetics and population modelling. Also includes exercises. more...
Nonmeasurable Sets and Functionsby Alexander Kharazishvili
Elsevier 2004; US$ 175.00The book is devoted to various constructions of sets which are nonmeasurable with respect to invariant (more generally, quasi-invariant) measures. Our starting point is the classical Vitali theorem stating the existence of subsets of the real line which are not measurable in the Lebesgue sense. This theorem stimulated the development of the following interesting topics in mathematics: 1. Paradoxical decompositions of sets in finite-dimensional Euclidean spaces; 2. The theory of non-real-valued-measurable cardinals; 3. The theory of invariant (quasi-invariant) extensions of invariant (quasi-invariant) measures. These topics are under consideration in the book. The role of nonmeasurable sets (functions) in point set theory and real analysis... more...
A Primer of Lebesgue Integrationby H. S. Bear
Elsevier 2001; US$ 78.95The Lebesgue integral is now standard for both applications and advanced mathematics. This books starts with a review of the familiar calculus integral and then constructs the Lebesgue integral from the ground up using the same ideas. A Primer of Lebesgue Integration has been used successfully both in the classroom and for individual study. Bear presents a clear and simple introduction for those intent on further study in higher mathematics. Additionally, this book serves as a refresher providing new insight for those in the field. The author writes with an engaging, commonsense style that appeals to readers at all levels. more...
Geometric Measure Theoryby Frank Morgan
Elsevier 2000; US$ 112.00Geometric measure theory has become increasingly essential to geometry as well as numerous and varied physical applications. The third edition of this leading text/reference introduces the theory, the framework for the study of crystal growth, clusters of soap bubbles, and similar structures involving minimization of energy. Over the past thirty years, this theory has contributed to major advances in geometry and analysis including, for example, the original proof of the positive mass conjecture in cosmology. This third edition of Geometric Measure Theory: A Beginner's Guide presents, for the first time in print, the proofs of the double bubble and the hexagonal honeycomb conjectures. Four new chapters lead the reader through treatments... more...
Gradient Flowsby Luigi Ambrosio; Nicola Gigli; Giuseppe Savaré
Springer 2005; US$ 52.95This book is devoted to the theory of gradient flows in the general framework of metric spaces, and in the more specific setting of the space of probability measures, which provide a surprising link between optimal transportation theory and many evolutionary PDE's related to (non)linear diffusion. more...
Measure Theoryby Vladimir I. Bogachev
Springer 2007; US$ 189.00Provides a presentation of modern measure theory. This book covers the classical theory of measure and integral, presenting the ideas that go back mainly to Lebesgue and also details the later developments, covering transformations of measures, conditional measures, and weak convergence of measures. more...
Measures, Integrals and Martingalesby René L. Schilling
Cambridge University Press 2005; US$ 52.00A concise undergraduate introduction to contemporary measure and integration theory as it is needed in many parts of analysis and probability. more...
Optimal Domain and Integral Extension of Operatorsby S. Okada; Werner J. Ricker; Enrique A. Sanchez Perez
Springer 2008; US$ 139.00This book deals with the analysis of linear operators from a quasi-Banach function space into a Banach space. The central theme is to extend the operator to as large a (function) space as possible, its optimal domain, and to take advantage of this in analyzing the original operator. Applications are given to Maurey-Rosenthal factorization of operators and to classical operators arising in commutative harmonic analysis. The main tool is the vector measure associated to such an operator, which produces a corresponding space of integrable functions and an integration operator. more...
The Bartle-Dunford-Schwartz Integralby Thiruvaiyaru V. Panchapagesan
Springer 2008; US$ 109.00This volume is a thorough and comprehensive treatise on vector measures. The functions to be integrated can be either 0, infinity]- or real- or complex-valued and the vector measure can take its values in arbitrary locally convex Hausdorff spaces. Moreover, the domain of the vector measure does not have to be a sigma-algebra: it can also be a delta-ring. The book contains not only a large amount of new material but also corrects various errors in well-known results available in the literature. It will appeal to a wide audience of mathematical analysts. more...









