Measure, integral, derivative a course on Lebesgue's theory Sergei Ovchinnikov

Format:

Book

Author/Creator:

Ovchinnikov, Sergeĭ

Series:

Universitext

Universitext 0172-5939

Language:

English

Subjects (All):

Lebesgue integral.

Mathematics.

Physical Sciences & Mathematics.

Calculus.

Measure and Integration.

Real Functions.

Analysis.

Local Subjects:

Mathematics.

Physical Sciences & Mathematics.

Calculus.

Measure and Integration.

Real Functions.

Analysis.

Physical Description:

1 online resource

Place of Publication:

New York, NY Springer ©2013

System Details:

PDF

text file

Summary:

This classroom-tested text is intended for a one-semester course in Lebesgue's theory. With over 180 exercises, the texttakes an elementary approach, making iteasily accessible toboth upper-undergraduate- and lower-graduate-level students. The three main topics presented are measure, integration, and differentiation, and the only prerequisite is a course in elementary real analysis. In order to keep the book self-contained, an introductory chapter is included with the intent to fill the gap between what the student may have learned before and what is required to fully understand the consequent text. Proofs of difficult results, such as the differentiability property of functions of bounded variations, are dissected into small steps in order to be accessible to students. With the exception of a few simple statements, all results are proven in the text. The presentation is elementary, where [sigma]-algebras are not used in the text on measure theory and Dini's derivatives are not used in the chapter on differentiation. However, all the main results of Lebesgue's theory are found in the book

This classroom-tested text is intended for a one-semester course in Lebesgue's theory. With over 180 exercises, the text takes an elementary approach, making it easily accessible to both upper-undergraduate- and lower-graduate-level students. The three main topics presented are measure, integration, and differentiation, and the only prerequisite is a course in elementary real analysis. In order to keep the book self-contained, an introductory chapter is included with the intent to fill the gap between what the student may have learned before and what is required to fully understand the consequent text. Proofs of difficult results, such as the differentiability property of functions of bounded variations, are dissected into small steps in order to be accessible to students. With the exception of a few simple statements, all results are proven in the text. The presentation is elementary, where σ-algebras are not used in the text on measure theory and Dini's derivatives are not used in the chapter on differentiation. However, all the main results of Lebesgue's theory are found in the book

Contents:

Preliminaries Lebesgue Measure Lebesgue Integration Differentiation and Integration

Notes:

Includes bibliographical references and index

Other Format:

Print version:

ISBN:

9781461471967

1461471966

1461471958

9781461471950

OCLC:

842882451

Access Restriction:

Restricted for use by site license