Step 28 of 37
The modern theory of integration, required for analysis and probability.
Topics, in order
- Sigma-algebras and measures
- Lebesgue measure
- Measurable functions and the Lebesgue integral
- Monotone and dominated convergence
- Product measures and Fubini's theorem
- Lp spaces
- Radon–Nikodym theorem
Learn from
- Stein and Shakarchi, Real Analysis
- Folland, Real Analysis
Move on when
You can state the dominated convergence theorem and apply it.