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Problems and Theorems in Analysis
Part 2
Integration
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On this page
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2.1 · The Integral as the Limit of a Sum of Rectangles
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2.2 · Inequalities
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2.3 · Some Properties of Real Functions
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2.4 · Various Types of Equidistribution
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2.5 · Functions of Large Numbers
Chapter 2.1
The Integral as the Limit of a Sum of Rectangles
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Section 1
The Lower and the Upper Sum
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Section 2
The Degree of Approximation
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Section 3
Improper Integrals Between Finite Limits
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Section 4
Improper Integrals Between Infinite Limits
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Section 5
Applications to Number Theory
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Section 6
Mean Values and Limits of Products
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Section 7
Multiple Integrals
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Chapter 2.2
Inequalities
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Section 1
Inequalities
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Section 2
Some Applications of Inequalities
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Chapter 2.3
Some Properties of Real Functions
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Section 1
Proper Integrals
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Section 2
Improper Integrals
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Section 3
Continuous, Differentiable, Convex Functions
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Section 4
Singular Integrals. Weierstrass' Approximation Theorem
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Chapter 2.4
Various Types of Equidistribution
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Section 1
Counting Function. Regular Sequences
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Section 2
Criteria of Equidistribution
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Section 3
Multiples of an Irrational Number
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Section 4
Distribution of the Digits in a Table of Logarithms and Related Questions
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Section 5
Other Types of Equidistribution
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Chapter 2.5
Functions of Large Numbers
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Section 1
Laplace's Method
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Section 2
Modifications of the Method
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Section 3
Asymptotic Evaluation of Some Maxima
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Section 4
Minimax and Maximin
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