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# Integral & Functional Analysis by Jie Xiao

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## Summary

Based on Integration and Metric Spaces and Functional Analysis, this book is useful for undergraduate students. This book assumes that the students have some familiarity with Introductory Calculus and Linear Algebra as well as the basic (direct, indirect) proof methods.

## Integral & Functional Analysis Summary

### Integral & Functional Analysis by Jie Xiao

This book is based on two closely-related courses. The first of these courses is Integration and Metric Spaces, and the second being Functional Analysis. Though the contents of Functional Analysis have been used for both an undergraduate course and an introductory graduate course, this text is designed primarily for undergraduate students. The prerequisites of this book are deliberately modest, and it is assumed that the students have some familiarity with Introductory Calculus and Linear Algebra plus the basic (direct, indirect) proof methods.

Preface; Preliminaries; Sets, Relations, Functions, Cardinals and Ordinals; Reals, Some Basic Theorems and Sequence Limits Problems; Riemann Integrals; Definitions, Examples, and Basic Properties; Algebraic Operations and the Darboux Criterion; Fundamental Theorem of Calculus; Improper Integrals Problems; Riemann-Stieltjes Integrals; Functions of Bounded Variation; Definition and Basic Properties; Nonexistence and Existence for Integrals; Evaluations of Integrals; Improper Cases Problems; Lebesgue-Radon-Stieltjes Integrals; Foundational Material; Essential Properties; Convergence Theorems; Extension via Measurability; Double and Iterated Integrals with Applications Problems; Metric Spaces; Metrizable Topology; Completeness; Compactness, Density and Separability Problems; Continuous Maps; Criteria for Continuity; Continuous Maps on Compact or Connected Spaces; Sequences of Mappings; Contractions; Equivalence of Metric Spaces Problems; Normed Linear Spaces; Linear Spaces, Norms and Quotient Spaces; Finite Dimensional Spaces; Bounded Linear Operators; Linear Functionals via Hahn-Banach Extension Problems; Banach Spaces via Operators and Functionals; Definition and Beginning Examples; Uniform Boundedness, Open Map and Closed Graph; Dual Banach Spaces by Examples; Weak and Weak Topologies; Compact and Dual Operators Problems; Hilbert Spaces and Their Operators; Definition, Examples and Basic Properties; Orthogonality, Orthogonal Complement and Duality; Orthonormal Sets and Bases; Five Special Bounded Operators; Compact Operators via the Spectrum; Problems; Hints and Solutions; References; Index.

NGR9781600217845
9781600217845
1600217842
Integral & Functional Analysis by Jie Xiao
New
Hardback
Nova Science Publishers Inc
2007-06-06
287
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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