Real Analysis: Modern Techniques and Their Applications, 2nd edition by Gerald B. Folland [pdf]

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A comprehensive study of real analysis and the applications it has, completely rewritten and expanded upon.

The genuine analysis is discussed in this new version of the widely used analysis book, which continues to cover the topic in greater detail than most other works on the subject, and at a more advanced level as well.

The measure and integration theory, point set topology, and the fundamentals of functional analysis are the primary themes of this book, which covers a variety of topics that are fundamental to a significant portion of contemporary analysis.

It does this by providing examples of how the general theories might be applied, as well as by introducing readers to other areas of analysis, such as the Fourier analysis, distribution theory, and probability theory.

Real Analysis: Modern Techniques and Their Applications, 2nd edition by Gerald B. Folland [Download pdf Below]

This version is improved not just in terms of its substance but also in terms of its scope, making it relevant to students studying subjects other than pure analysis as well as those with an interest in dynamic systems. Real Analysis: Modern Techniques and Their Applications, Second Edition is an excellent resource for students enrolled in graduate-level analysis courses due to the numerous exercises, wide bibliography, and review chapter on sets and metric spaces. Among the new features are:

  • Content regarding the n-dimensional Lebesgue integral has been updated.
  • A more convincing demonstration of Tychonoff’s theorem
  • Additional information regarding the Fourier analysis.
  • A brand new chapter that was recently written and is focused on differential equations and distributions.
  • Material that has been updated on the Hausdorff dimension and the fractal dimension.
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