Springer eBooks may be purchased by end-customers only and are sold without copy protection (DRM free). Instead, all eBooks include personalized watermarks. This means you can read the Springer eBooks across numerous devices such as Laptops, eReaders, and tablets.
You can pay for Springer eBooks with Visa, Mastercard, American Express or Paypal.
After the purchase you can directly download the eBook file or read it online in our Springer eBook Reader. Furthermore your eBook will be stored in your MySpringer account. So you can always re-download your eBooks.
(net)
price for USA
ISBN 978-1-4471-5122-7
digitally watermarked, no DRM
Included Format: PDF and EPUB
download immediately after purchase
Softcover (also known as softback) version.
You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.
Standard shipping is free of charge for individual customers.
(net)
price for USA
ISBN 978-1-4471-5121-0
free shipping for individuals worldwide
usually dispatched within 3 to 5 business days
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 detailed introduction to Lebesgue measure and integration as well as the classical results concerning integrals of multivariable functions. It examines the concept of the Hausdorff measure, the properties of the area on smooth and Lipschitz surfaces, the divergence formula, and Laplace's method for finding the asymptotic behavior of integrals. The general theory is then applied to harmonic analysis, geometry, and topology. Preliminaries are provided on probability theory, including the study of the Rademacher functions as a sequence of independent random variables.
The book contains more than 600 examples and exercises. The reader who has mastered the first third of the book will be able to study other areas of mathematics that use integration, such as probability theory, statistics, functional analysis, partial probability theory, statistics, functional analysis, partial differential equations and others.
Real Analysis: Measures, Integrals and Applications is intended for advanced undergraduate and graduate students in mathematics and physics. It assumes that the reader is familiar with basic linear algebra and differential calculus of functions of several variables.
Content Level » Graduate
Keywords » Fourier Analysis - Geometry - Measure and Integration - Real Functions
Related subjects » Analysis - Geometry & Topology
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.
Get alerted on new Springer publications in the subject area of Measure and Integration.