general integration and measure

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General Integration And Measure

Author : Alan J. Weir
ISBN : 0521204070
Genre : Mathematics
File Size : 41. 75 MB
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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.

Lebesgue Integration And Measure

Author : Alan J. Weir
ISBN : 0521097517
Genre : Mathematics
File Size : 58. 20 MB
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A textbook for the undergraduate who is meeting the Lebesgue integral for the first time, relating it to the calculus and exploring its properties before deducing the consequent notions of measurable functions and measure.

An Introduction To Measure And Integration

Author : Inder K. Rana
ISBN : 0821883917
Genre : Lebesgue integral
File Size : 71. 2 MB
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Introduction To Measure And Integration

Author : S. J. Taylor
ISBN : 0521098041
Genre : Mathematics
File Size : 26. 87 MB
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This paperback, gives a self-contained treatment of the theory of finite measures in general spaces at the undergraduate level.

Measure Theory And Integration

Author : Michael Eugene Taylor
ISBN : 9780821841808
Genre : Mathematics
File Size : 37. 11 MB
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This self-contained treatment of measure and integration begins with a brief review of the Riemann integral and proceeds to a construction of Lebesgue measure on the real line. From there the reader is led to the general notion of measure, to the construction of the Lebesgue integral on a measure space, and to the major limit theorems, such as the Monotone and Dominated Convergence Theorems. The treatment proceeds to $L^p$ spaces, normed linear spaces that are shown to be complete (i.e., Banach spaces) due to the limit theorems. Particular attention is paid to $L^2$ spaces as Hilbert spaces, with a useful geometrical structure. Having gotten quickly to the heart of the matter, the text proceeds to broaden its scope. There are further constructions of measures, including Lebesgue measure on $n$-dimensional Euclidean space. There are also discussions of surface measure, and more generally of Riemannian manifolds and the measures they inherit, and an appendix on the integration of differential forms. Further geometric aspects are explored in a chapter on Hausdorff measure. The text also treats probabilistic concepts, in chapters on ergodic theory, probability spaces and random variables, Wiener measure and Brownian motion, and martingales. This text will prepare graduate students for more advanced studies in functional analysis, harmonic analysis, stochastic analysis, and geometric measure theory.

Real Analysis

Author : J Yeh
ISBN : 9789814578561
Genre : Mathematics
File Size : 66. 83 MB
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This book presents a unified treatise of the theory of measure and integration. In the setting of a general measure space, every concept is defined precisely and every theorem is presented with a clear and complete proof with all the relevant details. Counter-examples are provided to show that certain conditions in the hypothesis of a theorem cannot be simply dropped. The dependence of a theorem on earlier theorems is explicitly indicated in the proof, not only to facilitate reading but also to delineate the structure of the theory. The precision and clarity of presentation make the book an ideal textbook for a graduate course in real analysis while the wealth of topics treated also make the book a valuable reference work for mathematicians. The book is also very helpful to graduate students in statistics and electrical engineering, two disciplines that apply measure theory.

Integration Measure And Probability

Author : H. R. Pitt
ISBN : 9780486488158
Genre : Mathematics
File Size : 62. 43 MB
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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.

A Primer Of Lebesgue Integration

Author : Herbert Stanley Bear
ISBN : 0120839717
Genre : Mathematics
File Size : 78. 33 MB
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"This succcssful text offers a reader-friendly approach to Lebesgue integration. - It is designed for advanced undergraduates, beginning graduate students, or advanced readers who may have forgotten one or two details from their real analysis courses."--BOOK JACKET.

Lebesgue Integration

Author : J.H. Williamson
ISBN : 9780486789774
Genre : Mathematics
File Size : 24. 58 MB
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This concise introduction to Lebesgue integration is geared toward advanced undergraduate math majors and may be read by any student possessing some familiarity with real variable theory and elementary calculus. The self-contained treatment features exercises at the end of each chapter that range from simple to difficult. The approach begins with sets and functions and advances to Lebesgue measure, including considerations of measurable sets, sets of measure zero, and Borel sets and nonmeasurable sets. A two-part exploration of the integral covers measurable functions, convergence theorems, convergence in mean, Fourier theory, and other topics. A chapter on calculus examines change of variables, differentiation of integrals, and integration of derivatives and by parts. The text concludes with a consideration of more general measures, including absolute continuity and convolution products. Dover (2014) republication of the edition originally published by Holt, Rinehart & Winston, New York, 1962. See every Dover book in print at www.doverpublications.com

Lebesgue Measure And Integration

Author : P. K. Jain
ISBN : UOM:39076000487426
Genre : Mathematics
File Size : 31. 59 MB
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