Real Analysis Book by Aliprantis and Burkinshaw

The new, 3rd Edition of this success-full text covers the fundamental theory of integration in a very  clear, well-organized manner. The authors gift an original and extremely sensible / practical synthesis of the "Daniell method" and therefore the theoretic approach. It is the perfect text for  college boy or undergraduate and first graduate courses in real analysis.
This edition offers a replacement chapter on Hilbert Spaces areas  and integrates over a hundred and fifty (150) new exercises. New and varied examples are enclosed for every chapter. Students are challenged by the over 600 exercises. Topics r treated strictly, illustrated by examples, and offer a clear connection between real and functional analysis.

This text are often utilized in combination with the authors' issues in Real Analysis, 2nd Edition, also published by Academic Press, which offers complete solutions to all exercises in the Principles text.
Key Features:
* Gives a unique presentation of integration theory
* Over  a hundred and fifty (150) new exercises integrated throughout the text
* Presents a new chapter on Hilbert Spaces
* Provides a rigorous introduction to measure theory
* Illustrated with new and varied examples in every chapter
* Introduces topological ideas in a friendly manner
* Offers a transparent affiliation between real and function analysis
* Includes brief biographies of mathematicians
"All altogether , this is often  a gorgeous choice and a masterfully balanced presentation of the basic of measure and integration theory which may be grasped simply by the student or scholar."
--J. Lorenz in Zentralblatt für Mathematik
"...a clear and precise treatment of the subject. There are many exercises of varying degrees of difficulty. I highly recommend this book for classroom use."
--CASPAR GOFFMAN, Department of Mathematics, Purdue University

Real Analysis Book by H.L Royden

Real Analysis, 4th Edition, covers the basic material that every reader should know in the classical theory of functions of a real variable, measure and integration theory, and some of the more important and elementary topics in normally topology and normed linear  theory. This text assumes a general background in math and familiarity with the basic ideas of research.
Classical theory of functions, together with the classical Banach spaces; General topology and therefore the theory of general Banach spaces; Abstract treatment of integration  and measure
For all readers interested in real analysis.
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