Real Analysis: Measures, Integrals and Applications

• Main Authors: Makarov, Boris. (Author), Podkorytov, Anatolii. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: London : Springer London : Imprint: Springer, 2013.
• Series: Universitext,
• Subjects: Mathematics.; Fourier analysis.; Geometry.; Measure and Integration.; Fourier Analysis.; Real Functions.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-1-4471-5122-7

Real Analysis: Measures, Integrals and Applications is devoted to the basics of integration theory and its related topics. The main emphasis is made on the properties of the Lebesgue integral and various applications both classical and those rarely covered in literature. � This book provides a detai...

Table of Contents:

• Measure
• The Lebesgue Model
• Measurable Functions
• The Integral
• The Product Measure
• Change of Variables in an Integral
• Integrals Dependent on a Parameter
• Surface Integrals
• Approximation and Convolution of the Space
• Fourier Series and the Fourier Transform
• Charges. The Radon-Nikodym Theory
• Integral Representation of Linear Functionals
• Appendices.