- eBook:Real Analysis: Measure Theory, Integration, and Hilbert Spaces (Princeton Lectures in Analysis, Book 3)
- Author:Elias M. Stein, Rami Shakarchi
- Data:April 3, 2005
- Pages:424 pages
After setting forth the basic facts of measure theory, Lebesgue integration, and differentiation on Euclidian spaces, the authors move to the elements of Hilbert space, via the L2 theory. They next present basic illustrations of these concepts from Fourier analysis, partial differential equations, and complex analysis. The final part of the book introduces the reader to the fascinating subject of fractional-dimensional sets, including Hausdorff measure, self-replicating sets, space-filling curves, and Besicovitch sets. Each chapter has a series of exercises, from the relatively easy to the more complex, that are tied directly to the text. A substantial number of hints encourage the reader to take on even the more challenging exercises.
As with the other volumes in the series, Real Analysis is accessible to students interested in such diverse disciplines as mathematics, physics, engineering, and finance, at both the undergraduate and graduate levels.
Chapter 2. Integration Theory
Chapter 3. Differentiation and Integration
Chapter 4. Hilbert Spaces: An Introduction
Chapter 5. Hilbert Spaces: Several Examples
Chapter 6. Abstract Measure and Integration Theory
Chapter 7. Hausdorff Measure and Fractals