Measure and Integration : An Introduction / by Satya N. Mukhopadhyay, Subhasis Ray.

Format:

Book

Author/Creator:

Mukhopadhyay, Satya N.

Contributor:

Ray, Subhasis.

Series:

University Texts in the Mathematical Sciences, 2731-9326

Language:

English

Subjects (All):

Measure theory.

Associative rings.

Associative algebras.

Functions of real variables.

Measure and Integration.

Associative Rings and Algebras.

Real Functions.

Local Subjects:

Measure and Integration.

Associative Rings and Algebras.

Real Functions.

Physical Description:

1 online resource (647 pages)

Edition:

1st ed. 2025.

Place of Publication:

Singapore : Springer Nature Singapore : Imprint: Springer, 2025.

Summary:

Designed for senior undergraduate and graduate students in mathematics, this textbook offers a comprehensive exploration of measure theory and integration. It acts as a pivotal link bridging the Riemann integral and the Lebesgue integral, with a primary focus on tracing the evolution of measure and integration from their historical roots. A distinctive feature of the book is meticulous guidance, providing a step-by-step journey through the subject matter, thus rendering complex concepts more accessible to beginners. A fundamental grasp of differential and integral calculus, as well as Riemann integration, is recommended to ensure a smoother comprehension of the material. This textbook comprises 10 well-structured chapters, each thoughtfully organized to lead students from fundamental principles to advanced complexities. Beginning with the establishment of Lebesgue’s measure on the real line and an introduction to measurable functions, the book then delves into exploring the cardinalities of various set classes. As readers progress, the subtleties of the Lebesgue integral emerge, showcasing its generalization of the Riemann integral and its unique characteristics in higher dimensions. One of the book’s distinctive aspects is its indepth comparison of the Lebesgue integral, improper Riemann integral, and Newton integral, shedding light on their distinct qualities and relative independence. Subsequent chapters delve into the realm of general measures, Lebesgue-Stieltje's measure, Hausdorff ’s measure, and the concept of measure and integration in product spaces. Furthermore, the book delves into function spaces, such as �������� spaces, and navigates the intricacies of signed and complex measures, providing students with a comprehensive foundation in this vital area of mathematics.

Contents:

Preliminaries

Lebesgue Measure on Real Line

Measurable Functions

More about Sets and Functions

The Lebesgue Integral

Differentiation of Functions

Lebesgue measure and integration in RN

General Measure and Outer Measure

Function Spaces

Signed Measure and Complex Measure.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

9789819725113

OCLC:

1490382476