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Real Analysis: Measure Theory, Integration, and Hilbert Spaces
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Real Analysis: Measure Theory, Integration, and Hilbert Spaces (Princeton Lectures in Analysis #3)

4.0 of 5 stars 4.00  ·  rating details  ·  23 ratings  ·  1 review
"Real Analysis" is the third volume in the Princeton Lectures in Analysis, a series of four textbooks that aim to present, in an integrated manner, the core areas of analysis. Here the focus is on the development of measure and integration theory, differentiation and integration, Hilbert spaces, and Hausdorff measure and fractals. This book reflects the objective of the se ...more
Hardcover, 424 pages
Published April 3rd 2005 by Princeton University Press (first published March 14th 2005)
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This book is a much more pleasant and approachable introduction to Measure theory than the usual grad school texts (Rudin, Royden, etc.) The description is clear and detailed, and there are plenty of illustrations to augment the proofs. My two complaints are:

(i) It often references earlier volumes in Stein's series with little or no explanation of what the reference is - since many readers don't own volumes I-III, it would be useful to at least have the referenced result stated in some summary f
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Other Books in the Series

Princeton Lectures in Analysis (4 books)
  • Fourier Analysis: An Introduction
  • Complex Analysis
  • Functional Analysis: Introduction to Further Topics in Analysis
Complex Analysis Fourier Analysis: An Introduction Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals. (PMS-43) Complex Analysis Singular Integrals and Differentiability Properties of Functions (PMS-30)

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