Kindly note that we have put a lot of effort into researching the best books on Normed Linear Spaces and Theory of Integration subject and came out with a recommended list of top 10 best books. The table below contains the Name of these best books, their authors, publishers and an unbiased review of books on "Normed Linear Spaces and Theory of Integration" as well as links to the Amazon website to directly purchase these books. As an Amazon Associate, we earn from qualifying purchases, but this does not impact our reviews, comparisons, and listing of these top books; the table serves as a ready reckoner list of these best books.
1. “Real Analysis” by H L Royden
“Real Analysis” Book Review: This book is for undergraduate students. This book starts with a basic introduction on classical theory of functions of a real variable. This book gives a description on measure and integration theory. This book gives information on general topology and the theory of general Banach spaces. A detailed explanation on normed linear space theory is given in this book. This book contains examples which helps in understanding of concepts.


2. “Measure Theory” by P R Halmos
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“Measure Theory” Book Review: This book is for graduate students. This book contains twelve chapters with references, bibliography and indexes at the end. This book gives descriptions on sets, classes and rings in algebra. An indepth explanation on measures on rings and intervals and their properties have been given in this book. Measurable functions and their properties have been discussed in detail. Different integration techniques and set functions have been described in this book. A detailed explanation on probability and locally compact spaces is given. Product spaces and topology have been explained in this book.


3. “Measure and Integration” by S K Berberian
“Measure and Integration” Book Review: This book is for graduate level students. This book provides an indepth discussion on the theory of measure and integration. convergence theorems, RieszFischer theorem, Fubini’s theorem, RadonNikodym theorem have been explained in this book. This book provides a description of the RieszMarkoff theorem and Haar measure on a locally compact group. The generalization of the Riemman/Riemman Stieltjes integrals have been discussed in depth. This book includes examples which are good for understanding.


4. “Introduction to Functional Analysis” by A E Taylor
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“Introduction to Functional Analysis” Book Review: This book includes the basic principles of functional analysis. Major chapters included are banach algebras, and material on weak topologies and duality, equicontinuity, the KreinMilman theorem. Other topics discussed are closed unbounded linear operators and the theory of Fredholm operators. Illustrations and examples are added for better understanding. This book can be referred to by graduate students of mathematics.


5. “Mathematical Methods: Linear Algebra, Normed Spaces, Distributions, Integration (Dover Books on Mathematics)” by Jacob Korevaar
“Mathematical Methods: Linear Algebra, Normed Spaces, Distributions, Integration (Dover Books on Mathematics)” Book Review: This book discusses advanced mathematical methods. Major topics mentioned are orthogonal series, linear operators in Hilbert space, integral equations and partial differential equations. Other topics mentioned are basic concepts of vector spaces, linear transformation, properties of Lebesgue integral functions. Illustrative examples and diagrams are added which are good for understanding. This book is beneficial for applied mathematics and graduate physical sciences students.


6. “Analysis in Vector Spaces: Solutions Manual” by Mustafa A Akcoglu and Paul F A Bartha
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“Analysis in Vector Spaces: Solutions Manual” Book Review: This book provides the introduction to calculus in vector spaces. Major chapters introduced are sets and functions, real numbers, vector functions, normed vector spaces and derivatives. Other topics mentioned are diffeomorphisms and manifolds, higherorder derivatives, multiple integrals and integration on modules. Graphs and equations are discussed in a detailed manner. Examples are added for students’ practice. This book can be used by students studying mathematics, physics, computer science and engineering.


7. “Methods in the Theory of Hereditarily Indecomposable Banach Spaces (Memoirs of the American Mathematical Society)” by Spiros Argyros and Andreas Tolias
“Methods in the Theory of Hereditarily Indecomposable Banach Spaces (Memoirs of the American Mathematical Society)” Book Review: This book includes general methods of producing hereditarily indecomposable banach spaces. Important chapters included are conjugate operator of the quotient map, weakly compact operator and the space of bounded linear operators. All the methods are discussed in detail. This book is suitable for advanced mathematics students.


8. “Basic Real Analysis” by Houshang H Sohrab
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“Basic Real Analysis” Book Review: This book explains the fundamental principles of real analysis of calculus. Major chapters included are set theory, sequences and series of real numbers, limits of functions, topology of r and continuity. Other topics mentioned are metric spaces, the derivative, the Reimann integral and sequences of series of functions. Problems are added at the end of every chapter to test the students’ knowledge. This book is useful for mathematics and engineering students.


9. “Differential Calculus in Normed Linear Spaces (Texts and Readings in Mathematics)” by Kalyan Mukherjea
“Differential Calculus in Normed Linear Spaces (Texts and Readings in Mathematics)” Book Review: This book consists of topics on advanced calculus from a geometric point of view. Chapters mentioned are linear transformation between normed linear spaces, the Inverse and Implicit function theorems, convergence of sequences and series of real numbers. Applications and examples are included for students’ practice. This book can be useful for mathematics, physics and engineering students.


10. “Four NonLinear Problems on Normed Spaces – Volume I” by Francisco Garcia Pacheco
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“Four NonLinear Problems on Normed Spaces – Volume I” Book Review: This book discusses 4 nonlinear problems on normal spaces. The problems included are the lineability problem for functionals (Aron and Gurariy, 2004) and the nowhere density problem for functionals (Enflo, 2005). Other 2 problems mentioned are the minimumnorm problem for translations (Aizpuru and GarciaPacheco, 2003) and the banachmazur conjecture for rotations (Banach and Mazur, 1932). All the problems are discussed in detail and proper manner. This book can be referred to by advanced applied mathematics students.


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