دانلود کتاب The Lebesgue Integral for Undergraduates

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Cover
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Copyright
Title
Series
Contents
Preface
Introduction
1 Lebesgue Integrable Functions
1.1 Two Infinities: Countable and Uncountable
1.2 A Taste of Measure Theory
1.3 Lebesgue\'s Integral for Step Functions
1.4 Limits
1.5 The Lebesgue Integral and L1
Notes for Chapter 1
2 Lebesgue\'s Integral Compared to Riemann\'s
2.1 The Riemann Integral
2.2 Properties of the Lebesgue Integral
2.3 Dominated Convergence and Further Properties of the Integral
2.4 Application: Fourier Series
Notes for Chapter 2
3 Function Spaces
3.1 The Spaces Lp
3.2 The Hilbert Space Properties of L2 and l2
3.3 Orthonormal Basis for a Hilbert Space
3.4 Application: Quantum Mechanics
Notes for Chapter 3
4 Measure Theory
4.1 Lebesgue Measure
4.2 Lebesgue Integrals with Respect to Other Measures
4.3 The Hilbert Space L2(μ)
4.4 Application: Probability
Notes for Chapter 4
5 Hilbert Space Operators
5.1 Bounded Linear Operators on L2
5.2 Bounded Linear Operators on General Hilbert Spaces
5.3 The Unilateral Shift Operator
5.4 Application: A Spectral Theorem Example
Notes for Chapter 5
Solutions to Selected Problems
Bibliography
Index