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Foundations of Real and Abstract Analysis

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Foundations of Real and Abstract Analysis

4.85 30,856 ratings · 5,249 reviews
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Overview: The core chapters of this volume provide a complete course on metric, normed, and Hilbert spaces, and include many results and exercises seldom found in texts on analysis at this level. The author covers an unusually wide range of material in a clear and concise format including elementary real analysis, Lebesgue integration on R, and an introduction to functional analysis. This makes a versatile text also suited for courses on real analysis, metric spaces, abstract analysis, and modern analysis. The book begins with a comprehensive chapter providing a fast-paced course on real analysis, and is followed by an introduction to the Lebesgue integral. This provides a reference for later chapters as well as an introduction for students with only the typical sequence of undergraduate calculus courses as prerequisites. Other features include a chapter introducing functional analysis, the Hahn-Banach theorem and duality, separation theorems, the Baire Category Theorem, the Open Mapping Theorem and their consequences, and unusual applications such as weak solutions of the Dirichlet Problem and Pareto optimality in Mathematical Economics.; Of special interest is the unique collection of nearly 750 exercises, many with guidelines for their solutions. The exercises include applications and extensions of the main propositions and theorems, results that fill in gaps in proofs or that prepare for proofs later in the book, pointers to new branches of the subject, and difficult challenges for the very best students.

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Pages 322
Publisher Springer
Published January 1, 1998
ISBN 16746402
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D S Bridges
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D S Bridges
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D S Bridges is a writer and avid reader based in the Pacific Northwest. Before pursuing writing full-time, they spent over a decade working in education. When not working on their next book, D S Bridges can usually be found hiking with their dog or trying out new coffee shops in their neighborhood.

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Robert Taylor
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Carol Johnson October 28, 2025
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Took a moment to build, but the payoff was spectacular. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A wonderful companion for a quiet weekend.
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Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
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Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
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A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers.
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A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
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A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
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Linda Moore May 09, 2025
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Mark Scott May 02, 2025
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Sandra Miller April 26, 2025
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Ryan Moore
Ryan Moore December 05, 2025
Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
Jessica Baker
Jessica Baker February 10, 2024
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Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
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Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
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Michelle Ramirez July 10, 2024
I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
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Lisa Flores October 27, 2025
Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
Kevin Jackson
Kevin Jackson August 10, 2024
Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
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Steven Williams July 11, 2024
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Lisa Gomez
Lisa Gomez June 25, 2024
Excellent, though slightly flawed. It held my rapt attention, even when certain twists were telegraphed. Quite impressive overall.
Rebecca Moore
Rebecca Moore November 26, 2024
Excellent, though slightly flawed. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend.
Barbara Baker
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Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
Linda Martinez
Linda Martinez January 12, 2025
Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
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Margaret Davis September 25, 2025
A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. I would highly recommend this to discerning readers.
Mary Rivera
Mary Rivera June 04, 2024
Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Andrew Hall
Andrew Hall April 28, 2025
A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. A solid 4 stars from me.
Richard Wilson
Richard Wilson March 23, 2024
A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend.
Patricia Cruz
Patricia Cruz May 22, 2025
A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
Andrew Rivera
Andrew Rivera November 27, 2024
Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
Sarah Hill
Sarah Hill February 02, 2024
A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers.
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Kenneth Smith October 23, 2024
Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
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Ryan Jackson May 01, 2025
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
William Young
William Young September 24, 2024
Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
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Laura Sanchez August 31, 2024
Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
Sarah Robinson
Sarah Robinson September 01, 2024
Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
Paul Collins
Paul Collins December 29, 2025
A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
Paul Clark
Paul Clark April 09, 2025
Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
Melissa Smith
Melissa Smith January 16, 2025
A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. A solid 4 stars from me.
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Melissa Smith February 06, 2025
I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
Susan Gonzalez
Susan Gonzalez April 27, 2025
Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
Michael Evans
Michael Evans November 18, 2024
A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
Charles Evans
Charles Evans June 09, 2025
A very strong entry. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend.
Paul Clark
Paul Clark May 01, 2025
Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
Jessica Wilson
Jessica Wilson November 27, 2024
A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
Michael Nguyen
Michael Nguyen February 12, 2024
Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
Margaret Taylor
Margaret Taylor April 13, 2024
A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. I would highly recommend this to discerning readers.
Donald Moore
Donald Moore December 16, 2025
Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
Matthew Thompson
Matthew Thompson May 26, 2024
A very strong entry. It held my rapt attention, even when certain twists were telegraphed. Quite impressive overall.
Kimberly Edwards
Kimberly Edwards March 26, 2024
Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
Melissa Diaz
Melissa Diaz February 09, 2024
I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. A solid 4 stars from me.
Michael Rivera
Michael Rivera July 14, 2024
Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
Joshua Hill
Joshua Hill January 27, 2024
I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
Jacob Torres
Jacob Torres December 15, 2025
Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
Jennifer Diaz
Jennifer Diaz September 29, 2024
A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
Christopher Anderson
Christopher Anderson October 06, 2024
A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. A solid 4 stars from me.
Jacob White
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I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
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