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Measure-theoretic calculus in abstract spaceson the playground of infinite-dimensional spaces /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Measure-theoretic calculus in abstract spacesby Zigang Pan.
其他題名:	on the playground of infinite-dimensional spaces /
作者:	Pan, Zigang.
出版者:	Cham :Springer International Publishing :2023.
面頁冊數:	xxvii, 933 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Measure theory.
電子資源:	https://doi.org/10.1007/978-3-031-21912-2
ISBN:	9783031219122$q(electronic bk.)

Measure-theoretic calculus in abstract spaceson the playground of infinite-dimensional spaces /
Pan, Zigang.

Measure-theoretic calculus in abstract spaceson the playground of infinite-dimensional spaces /[electronic resource] :by Zigang Pan. - Cham :Springer International Publishing :2023. - xxvii, 933 p. :ill., digital ;24 cm.

This monograph provides a rigorous, encyclopedic treatment of the fundamental topics in real analysis, functional analysis, and measure theory. The result of many years of the author's careful and extensive work, this text synthesizes and builds upon the existing literature in an effort to develop and solidify the theory of measure-theoretic calculus in abstract spaces. Standard results and proofs are illustrated in general abstract settings under rigorous treatment, and numerous ancillary topics are also covered in detail, such as functional analytic treatment of optimization, probability theory, and the theory of Sobolev spaces. Applied mathematicians and researchers working in control theory, operations research, economics, optimization theory, and many other areas will find this text to be a comprehensive and invaluable resource. It can also serve as an analysis textbook for graduate-level students.

ISBN: 9783031219122$q(electronic bk.)

Standard No.: 10.1007/978-3-031-21912-2doiSubjects--Topical Terms:

182047
Measure theory.

LC Class. No.: QA312

Dewey Class. No.: 515.42

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520 $a This monograph provides a rigorous, encyclopedic treatment of the fundamental topics in real analysis, functional analysis, and measure theory. The result of many years of the author's careful and extensive work, this text synthesizes and builds upon the existing literature in an effort to develop and solidify the theory of measure-theoretic calculus in abstract spaces. Standard results and proofs are illustrated in general abstract settings under rigorous treatment, and numerous ancillary topics are also covered in detail, such as functional analytic treatment of optimization, probability theory, and the theory of Sobolev spaces. Applied mathematicians and researchers working in control theory, operations research, economics, optimization theory, and many other areas will find this text to be a comprehensive and invaluable resource. It can also serve as an analysis textbook for graduate-level students.
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