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An Introduction to Measure and Integration
The important basic topics are all covered: the Fundamental Theorem of Calculus, Fubini's Theorem, L[subscript p] spaces, the Radon-Nikodym Theorem, change of variables formulas, and so on." "The book is written in an informal style to make the subject matter easily accessible. Concepts are developed with the help of motivating examples, probing questions, and many exercises. It would be suitable as a textbook for an introductory course on the topic or for self-study."--BOOK JACKET.
From Numbers to Analysis
"This book is recommended to students and instructors looking for a very well-organized introduction to the foundations of analysis".Acta Sci. Math., 1999
A Modern Theory of Integration
The theory of integration is one of the twin pillars on which analysis is built. The first version of integration that students see is the Riemann integral. Later, graduate students learn that the Lebesgue integral is ``better'' because it removes some restrictions on the integrands and the domains over which we integrate. However, there are still drawbacks to Lebesgue integration, for instance, dealing with the Fundamental Theorem of Calculus, or with ``improper'' integrals. This book is an introduction to a relatively new theory of the integral (called the ``generalized Riemann integral'' or the ``Henstock-Kurzweil integral'') that corrects the defects in the classical Riemann theory and b...
The Elements of Integration and Lebesgue Measure
Consists of two separate but closely related parts. Originally published in 1966, the first section deals with elements of integration and has been updated and corrected. The latter half details the main concepts of Lebesgue measure and uses the abstract measure space approach of the Lebesgue integral because it strikes directly at the most important results—the convergence theorems.
Measure Theory and Integration
This text approaches integration via measure theory as opposed to measure theory via integration, an approach which makes it easier to grasp the subject. Apart from its central importance to pure mathematics, the material is also relevant to applied mathematics and probability, with proof of the mathematics set out clearly and in considerable detail. Numerous worked examples necessary for teaching and learning at undergraduate level constitute a strong feature of the book, and after studying statements of results of the theorems, students should be able to attempt the 300 problem exercises which test comprehension and for which detailed solutions are provided. - Approaches integration via measure theory, as opposed to measure theory via integration, making it easier to understand the subject - Includes numerous worked examples necessary for teaching and learning at undergraduate level - Detailed solutions are provided for the 300 problem exercises which test comprehension of the theorems provided
Introduction to Numerical Analysis
On the occasion of this new edition, the text was enlarged by several new sections. Two sections on B-splines and their computation were added to the chapter on spline functions: Due to their special properties, their flexibility, and the availability of well-tested programs for their computation, B-splines play an important role in many applications. Also, the authors followed suggestions by many readers to supplement the chapter on elimination methods with a section dealing with the solution of large sparse systems of linear equations. Even though such systems are usually solved by iterative methods, the realm of elimination methods has been widely extended due to powerful techniques for h...
E-Government Services Design, Adoption, and Evaluation
With the widespread knowledge and use of e-government, the intent and evaluation of e-government services continues to focus on meeting the needs and satisfaction of its citizens. E-Government Services Design, Adoption, and Evaluation is a comprehensive collection of research on assessment and implementation of electronic/digital government technologies in organizations. This book aims to supply academics, practitioners and professionals with the understanding of e-government and its applications and impact on organizations around the world.
Measures, Integrals and Martingales
This book, first published in 2005, introduces measure and integration theory as it is needed in many parts of analysis and probability.
