Author: Krzysztof Ostaszewski Publisher: American Mathematical Soc. ISBN: 0821824163 Category : Mathematics Languages : en Pages : 118
Book Description
This paper deals with the integration of abstract Henstock type. Eleven derivation bases on the plane are investigated, those built with triangles, rectangles, and regular rectangles, and the approximate bases. The relationships between the integration theories generated by them are found.
Author: Peng Yee Lee Publisher: World Scientific ISBN: 9814513792 Category : Mathematics Languages : en Pages : 192
Book Description
This is an introductory book on Henstock integration, otherwise known as generalized Riemann integral. It is self-contained and introductory. The author has included a series of convergence theorems for the integral, previously not available. In this book, he has also developed a technique of proof required to present the new as well as the classical results.
Author: Guillermo Curbera Publisher: Springer Science & Business Media ISBN: 3034602111 Category : Mathematics Languages : en Pages : 382
Book Description
This volume contains a selection of articles on the theme "vector measures, integration and applications" together with some related topics. The articles consist of both survey style and original research papers, are written by experts in thearea and present a succinct account of recent and up-to-date knowledge. The topic is interdisciplinary by nature and involves areas such as measure and integration (scalar, vector and operator-valued), classical and harmonic analysis, operator theory, non-commutative integration, andfunctional analysis. The material is of interest to experts, young researchers and postgraduate students.
Author: Ralph Henstock Publisher: World Scientific ISBN: 9789971504519 Category : Mathematics Languages : en Pages : 224
Book Description
This book is intended to be self-contained, giving the theory of absolute (equivalent to Lebesgue) and non-absolute (equivalent to Denjoy-Perron) integration by using a simple extension of the Riemann integral. A useful tool for mathematicians and scientists needing advanced integration theory would be a method combining the ideas of the calculus of indefinite integral and Riemann definite integral in such a way that Lebesgue properties can be proved easily.Three important results that have not appeared in any other book distinguish this book from the rest. First a result on limits of sequences under the integral sign, secondly the necessary and sufficient conditions for the various limits under the integral sign and thirdly the application of these results to ordinary differential equations. The present book will give non-absolute integration theory just as easily as the absolute theory, and Stieltjes-type integration too.
Author: Tuo Yeong Lee Publisher: World Scientific ISBN: 9814324582 Category : Mathematics Languages : en Pages : 325
Book Description
The Henstock?Kurzweil integral, which is also known as the generalized Riemann integral, arose from a slight modification of the classical Riemann integral more than 50 years ago. This relatively new integral is known to be equivalent to the classical Perron integral; in particular, it includes the powerful Lebesgue integral. This book presents an introduction of the multiple Henstock?Kurzweil integral. Along with the classical results, this book contains some recent developments connected with measures, multiple integration by parts, and multiple Fourier series. The book can be understood with a prerequisite of advanced calculus.
Author: E. Pap Publisher: Elsevier ISBN: 0080533094 Category : Mathematics Languages : en Pages : 1633
Book Description
The main goal of this Handbook isto survey measure theory with its many different branches and itsrelations with other areas of mathematics. Mostly aggregating many classical branches of measure theory the aim of the Handbook is also to cover new fields, approaches and applications whichsupport the idea of "measure" in a wider sense, e.g. the ninth part of the Handbook. Although chapters are written of surveys in the variousareas they contain many special topics and challengingproblems valuable for experts and rich sources of inspiration.Mathematicians from other areas as well as physicists, computerscientists, engineers and econometrists will find useful results andpowerful methods for their research. The reader may find in theHandbook many close relations to other mathematical areas: realanalysis, probability theory, statistics, ergodic theory,functional analysis, potential theory, topology, set theory,geometry, differential equations, optimization, variationalanalysis, decision making and others. The Handbook is a richsource of relevant references to articles, books and lecturenotes and it contains for the reader's convenience an extensivesubject and author index.
Author: Solomon Leader Publisher: CRC Press ISBN: 1482270862 Category : Mathematics Languages : en Pages : 372
Book Description
A comprehensive review of the Kurzweil-Henstock integration process on the real line and in higher dimensions. It seeks to provide a unified theory of integration that highlights Riemann-Stieljes and Lebesgue integrals as well as integrals of elementary calculus. The author presents practical applications of the definitions and theorems in each sec
Author: Krzysztof Ostaszewski
Author: Peng Yee Lee
Author: Guillermo Curbera
Author: Ralph Henstock
Author: Tuo Yeong Lee
Author: E. Pap
Author: Li Zhong
Author: Solomon Leader
Author: Peter S. Bullen
Author: V. Covachev