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Author : Angus Ellis Taylor
Publisher : Unknown
Page : 437 pages
File Size : 46,7 Mb
Release : 1970
Category : Calculus, Integral
ISBN : OCLC:848261749
Author : Angus Ellis Taylor
Publisher : Courier Corporation
Page : 451 pages
File Size : 45,9 Mb
Release : 1985-01-01
Category : Mathematics
ISBN : 9780486649887
Uniting a variety of approaches to the study of integration, a well-known professor presents a single-volume "blend of the particular and the general, of the concrete and the abstract." 1966 edition.
Author : Angus E. Taylor
Publisher : Unknown
Page : 472 pages
File Size : 46,7 Mb
Release : 1965
Category : Calculus, Integral
ISBN : UCAL:B5008504
Author : Angus E. Taylor
Publisher : Courier Corporation
Page : 456 pages
File Size : 51,7 Mb
Release : 2012-05-24
Category : Mathematics
ISBN : 0486152146
Presenting the various approaches to the study of integration, a well-known mathematics professor brings together in one volume "a blend of the particular and the general, of the concrete and the abstract." This volume is suitable for advanced undergraduates and graduate courses as well as for independent study. 1966 edition.
Author : Hassler Whitney
Publisher : Courier Corporation
Page : 402 pages
File Size : 49,6 Mb
Release : 2012-01-27
Category : Mathematics
ISBN : 9780486154701
Geared toward upper-level undergraduates and graduate students, this treatment of geometric integration theory consists of an introduction to classical theory, a postulational approach to general theory, and a section on Lebesgue theory. 1957 edition.
Author : Angus Ellis Taylor
Publisher : Unknown
Page : 472 pages
File Size : 44,6 Mb
Release : 1965
Category : Calculus, Integral
ISBN : MINN:31951000917426B
The real numbers. Point sets and sequences -- Euclidean space. Topology and continuous functions -- Abstract spaces -- The theory of measure -- The Lebesgue integral -- Integration by the Daniell method -- Iterated integrals and Fubini's theorem -- The theory of signed measures -- Functions of one real variable.
Author : Nicolas Lerner
Publisher : Springer
Page : 492 pages
File Size : 49,6 Mb
Release : 2014-07-09
Category : Mathematics
ISBN : 9783034806947
This textbook provides a detailed treatment of abstract integration theory, construction of the Lebesgue measure via the Riesz-Markov Theorem and also via the Carathéodory Theorem. It also includes some elementary properties of Hausdorff measures as well as the basic properties of spaces of integrable functions and standard theorems on integrals depending on a parameter. Integration on a product space, change of variables formulas as well as the construction and study of classical Cantor sets are treated in detail. Classical convolution inequalities, such as Young's inequality and Hardy-Littlewood-Sobolev inequality are proven. The Radon-Nikodym theorem, notions of harmonic analysis, classical inequalities and interpolation theorems, including Marcinkiewicz's theorem, the definition of Lebesgue points and Lebesgue differentiation theorem are further topics included. A detailed appendix provides the reader with various elements of elementary mathematics, such as a discussion around the calculation of antiderivatives or the Gamma function. The appendix also provides more advanced material such as some basic properties of cardinals and ordinals which are useful in the study of measurability.
Author : Patrick Muldowney
Publisher : Longman
Page : 136 pages
File Size : 52,8 Mb
Release : 1987
Category : Mathematics
ISBN : UOM:39015049290748
Author : Terence Tao
Publisher : American Mathematical Soc.
Page : 206 pages
File Size : 47,6 Mb
Release : 2021-09-03
Category : Education
ISBN : 9781470466404
This is a graduate text introducing the fundamentals of measure theory and integration theory, which is the foundation of modern real analysis. The text focuses first on the concrete setting of Lebesgue measure and the Lebesgue integral (which in turn is motivated by the more classical concepts of Jordan measure and the Riemann integral), before moving on to abstract measure and integration theory, including the standard convergence theorems, Fubini's theorem, and the Carathéodory extension theorem. Classical differentiation theorems, such as the Lebesgue and Rademacher differentiation theorems, are also covered, as are connections with probability theory. The material is intended to cover a quarter or semester's worth of material for a first graduate course in real analysis. There is an emphasis in the text on tying together the abstract and the concrete sides of the subject, using the latter to illustrate and motivate the former. The central role of key principles (such as Littlewood's three principles) as providing guiding intuition to the subject is also emphasized. There are a large number of exercises throughout that develop key aspects of the theory, and are thus an integral component of the text. As a supplementary section, a discussion of general problem-solving strategies in analysis is also given. The last three sections discuss optional topics related to the main matter of the book.
Author : Alan J. Weir
Publisher : CUP Archive
Page : 316 pages
File Size : 47,7 Mb
Release : 1974-11-14
Category : Mathematics
ISBN : 0521204070
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.
Author : Georges Valiron
Publisher : Unknown
Page : 128 pages
File Size : 49,5 Mb
Release : 1949
Category : Electronic
ISBN : OCLC:841868506
Author : Ernest William Hobson
Publisher : CUP Archive
Page : 804 pages
File Size : 49,9 Mb
Release : 1927
Category : Calculus
ISBN : 8210379456XXX
Author : Stanislaw Saks
Publisher : Courier Dover Publications
Page : 376 pages
File Size : 55,6 Mb
Release : 2005
Category : Mathematics
ISBN : PSU:000059103820
An excellent introduction to modern real variable theorem, this volume covers all the standard topics: theory, theory of measure, functions with general properties, and theory of integration, with emphasis on the Lebesgue integral and its related theory of derivation. The author begins with a discussion of the integral in an abstract space, covering additive classes of sets, measurable functions, integration of sequences of functions, and the Lebesgue decomposition of an additive function. Succeeding chapters cover Carath�odory measure; functions of bounded variation and the Lebesgue-Stieltjes integral; the derivation of additive functions of a set and of an interval; and major and minor functions and the Perron integral. Additional topics include functions of generalized bounded variation; Denjoy integrals; and derivates of functions of one or two real variables. This book will prove to be extremely useful as a course text or as supplementary reading to students of real variable theory and others interested in this branch of mathematics. Only a minimal background in elementary analysis is necessary, and the preface offers a helpful overview of the history of the theory of real functions.
Author : Ralph Henstock
Publisher : Unknown
Page : 288 pages
File Size : 51,5 Mb
Release : 1991
Category : Mathematics
ISBN : UOM:39015021856110
Every good mathematical book stands like a tree with its roots in the past and its branches stretching out towards the future. Whether the fruits of this tree are desirable and whether the branches will be quarried for mathematical wood to build further edifices, I will leave to the judgment of history. The roots of this book take nourishment from the concept of definite integration of continuous functions, where Riemann's method is the high water mark of the simpler theory.
Author : Anonim
Publisher : Bookboon
Page : 107 pages
File Size : 52,9 Mb
Release : 2024-06-18
Category : Electronic
ISBN : 9788776817183
