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The Lebesgue Integral

Zoltán Magyar
4.9/5 (24527 ratings)
Read Now Download Now ⏭ listen AudioBook
Description:The book presents the development of the Lebesgue integral in such a way that both usual approaches are explained. Namely, the Lebesgue integral can be built of a measure over a [sigma]-algebra (more generally, over any semiring, e.g. the intervals in the line or the bricks in [actual symbol not reproducible]), or of a so-called Daniell-functional which is the would-be integral on some nice functions (the prime examples are the Riemann integral and its usual generalizations, in particular, the Riemann-Stieltjes integral in several variables). The author deems the second approach more powerful, but the other approach and their relation are also discussed in detail in Part I. Part II treats Fubini's theorem with special attention to the boundaries of its validity. Part III explains localizability and contains some stronger versions of the Radon-Nikodym theorem due to the author. Finally, complex measures are discussed. A useful Index completes the book.This volume is recommended to those who are familiar with calculus and are interested in the field of Lebesgue integral and the related theory of measures. It may be useful both for those first meeting the topic and for those deepening its understanding. So we propose it to students and researchers in mathematics, physics, engineering, etc.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with The Lebesgue Integral. To get started finding The Lebesgue Integral, you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.
Pages
101
Format
PDF, EPUB & Kindle Edition
Publisher
Akadémia Kiadó
Release
—
ISBN
9630573466

The Lebesgue Integral

Zoltán Magyar
4.4/5 (1290744 ratings)
Read Now Download now ⏭ listen AudioBook
Description: The book presents the development of the Lebesgue integral in such a way that both usual approaches are explained. Namely, the Lebesgue integral can be built of a measure over a [sigma]-algebra (more generally, over any semiring, e.g. the intervals in the line or the bricks in [actual symbol not reproducible]), or of a so-called Daniell-functional which is the would-be integral on some nice functions (the prime examples are the Riemann integral and its usual generalizations, in particular, the Riemann-Stieltjes integral in several variables). The author deems the second approach more powerful, but the other approach and their relation are also discussed in detail in Part I. Part II treats Fubini's theorem with special attention to the boundaries of its validity. Part III explains localizability and contains some stronger versions of the Radon-Nikodym theorem due to the author. Finally, complex measures are discussed. A useful Index completes the book.This volume is recommended to those who are familiar with calculus and are interested in the field of Lebesgue integral and the related theory of measures. It may be useful both for those first meeting the topic and for those deepening its understanding. So we propose it to students and researchers in mathematics, physics, engineering, etc.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with The Lebesgue Integral. To get started finding The Lebesgue Integral, you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.
Pages
101
Format
PDF, EPUB & Kindle Edition
Publisher
Akadémia Kiadó
Release
—
ISBN
9630573466

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