Download PDF by Elias M. Stein,Rami Shakarchi: Real Analysis: Measure Theory, Integration, and Hilbert

By Elias M. Stein,Rami Shakarchi

ISBN-10: 0691113866

ISBN-13: 9780691113869

Real Analysis is the 3rd quantity within the Princeton Lectures in research, a chain of 4 textbooks that target to provide, in an built-in demeanour, the center components of research. the following the focal point is at the improvement of degree and integration idea, differentiation and integration, Hilbert areas, and Hausdorff degree and fractals. This publication displays the target of the sequence as a complete: to make simple the natural harmony that exists among a number of the elements of the topic, and to demonstrate the extensive applicability of rules of study to different fields of arithmetic and science.

After surroundings forth the fundamental proof of degree concept, Lebesgue integration, and differentiation on Euclidian areas, the authors stream to the weather of Hilbert area, through the L2 idea. They subsequent current simple illustrations of those options from Fourier research, partial differential equations, and intricate research. the ultimate a part of the ebook introduces the reader to the interesting topic of fractional-dimensional units, together with Hausdorff degree, self-replicating units, space-filling curves, and Besicovitch units. every one bankruptcy has a sequence of routines, from the fairly effortless to the extra advanced, which are tied on to the textual content. a considerable variety of tricks inspire the reader to tackle even the tougher exercises.

As with the opposite volumes within the sequence, Real Analysis is on the market to scholars drawn to such different disciplines as arithmetic, physics, engineering, and finance, at either the undergraduate and graduate levels.

Also to be had, the 1st volumes within the Princeton Lectures in Analysis:

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Real Analysis: Measure Theory, Integration, and Hilbert Spaces: Bk. 3 (Princeton Lectures in Analysis) by Elias M. Stein,Rami Shakarchi

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