Measure and Integration

Name: Measure and Integration
Brand: Springer, Berlin
SKU: 9789819725106
Price: 542.54 RON
Availability: InStock

An Introduction

Autor: Satya N. Mukhopadhyay, Subhasis Ray

Limbă:

Legare: Copertă tare

Editura: Springer, Berlin

Disponibilitate: În depozitul extern

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542.54 lei

Designed for senior undergraduate and graduate students in mathematics, this textbook offers a compr...

Informații despre carte

Autor

Satya N. Mukhopadhyay, Subhasis Ray

Limbă

engleză

Legare

Carte - Copertă tare

Publicat

2024

Pagini

320

EAN

9789819725106

Enbook ID

45304712

Editura

Springer, Berlin

Greutate

658

Dimensiuni

155 x 235

Descriere completă

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 higherdimensions.Moreover, approximate continuity is defined and used in the Lebesgue integral, just as continuity is used in the Riemann integral. This comparative analysis enhances the understanding of both integration methods. One of the book's distinctive aspects is its in-depth 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 Lp-spaces, and navigates the intricacies of signed and complex measures, providing students with a comprehensive foundation in this vital area of mathematics.

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Measure and Integration

An Introduction

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