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Measure Theory

Measure and integration, following Folland’s Real Analysis. Written as the course goes: a work in progress.

8 of 23 sections written

0Prologue

1. 0.1
   The Language of Set Theory
2. 0.2
   Orderings
3. 0.3
   Cardinality
4. 0.4
   More about Well Ordering
5. 0.5
   The Extended Real Number System
6. 0.6
   Metric Spaces

1Measures

1. 1.1
   Introduction
2. 1.2
   -algebras in progress
3. 1.3
   Measures
4. 1.4
   Outer Measures
5. 1.5
   Borel Measures on the Real Line

2Integration

1. 2.1
   Measurable Functions
2. 2.2
   Integration of Nonnegative Functions
3. 2.3
   Integration of Complex Functions
4. 2.4
   Modes of Convergence
5. 2.5
   Product Measures
6. 2.6
   The -dimensional Lebesgue Integral
7. 2.7
   Integration in Polar Coordinates

3Signed Measures and Differentiation

1. 3.1
   Signed Measures
2. 3.2
   The Lebesgue–Radon–Nikodym Theorem
3. 3.3
   Complex Measures
4. 3.4
   Differentiation on Euclidean Space
5. 3.5
   Functions of Bounded Variation