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This is the fourth and final volume in the Princeton Lectures in Analysis, a series of textbooks that aim to present, in an integrated manner, the core areas of analysis. They are, in order, Fourier Analysis: An Introduction; Complex Analysis; Real Analysis: Measure Theory, Integration, and Hilbert Spaces; and Functional Analysis: Introduction to Further Topics in Analysis. We mention without proof that the analysis in the previous section can be done using a Bernstein-Orlicz type argument, simplifying several steps in the proof shown. Beginning with the basic facts of functional analysis, this volume looks at Banach spaces, Lp spaces, and distribution theory, and highlights their roles in harmonic analysis. Functional Analysis: Introduction to Further Topics in Analysis Elias M. Stein and Rami Shakarchi This is the fourth and final volume in the Princeton Lectures in Analysis, a series of textbooks that aim to present, in an integrated manner, the core areas of analysis. 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Read online, or download in secure PDF or secure ePub format This is the fourth and final volume in the Princeton Lectures in Analysis, a series of textbooks that aim to present, in an integrated manner, the core areas of analysis. The authors then use the Baire category theorem .
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