Chen W.W.L. Introduction to Lebesgue Integration

Macquarie University, 1996. — 75 p.An introduction to some of the basic ideas in Lebesgue integration with the minimal use of measure theory.The real numbers and countability
The riemann integral
Point sets
The lebesgue integral
Monotone convergence theorem
Dominated convergence theorem
Lebesgue integrals on unbounded intervals
Measurable functions and measurable sets
Continuity and differentiability of lebesgue integrals
Double lebesgue integrals