Real Analysis: Modern Techniques and Their Applications

An in-depth look at real analysis and its applications-now expandedand revised.

This new edition of the widely used analysis book continues tocover real analysis in greater detail and at a more advanced levelthan most books on the subject. Encompassing several subjects thatunderlie much of modern analysis, the book focuses on measure andintegration theory, point set topology, and the basics offunctional analysis. It illustrates the use of the general theoriesand introduces readers to other branches of analysis such asFourier analysis, distribution theory, and probabilitytheory.

This edition is bolstered in content as well as in scope-extendingits usefulness to students outside of pure analysis as well asthose interested in dynamical systems. The numerous exercises,extensive bibliography, and review chapter on sets and metricspaces make Real Analysis: Modern Techniques and TheirApplications, Second Edition invaluable for students ingraduate-level analysis courses. New features include:
* Revised material on the n-dimensional Lebesgue integral.
* An improved proof of Tychonoff's theorem.
* Expanded material on Fourier analysis.
* A newly written chapter devoted to distributions and differentialequations.
* Updated material on Hausdorff dimension and fractal dimension.

• Algebraic Topology
• Abstract Algebra, 3rd Edition
• Real Analysis: Measure Theory, Integration, and Hilbert Spaces (Princeton Lectures in Analysis) (Bk. 3)
• Real & Complex Analysis
• Introduction to Smooth Manifolds (Graduate Texts in Mathematics, Vol. 218)
• Topology
• Partial Differential Equations: Second Edition (Graduate Studies in Mathematics)
• Probability: Theory and Examples (Cambridge Series in Statistical and Probabilistic Mathematics)
• Principles of Mathematical Analysis
• Cracking the GRE Mathematics Subject Test, 4th Edition