In this program
- Sigma-algebras, measurable functions, and measures
- Lebesgue integral
- Convergence theorems (MCT, Fatou, DCT)
- L^p spaces
- Hölder / Minkowski inequalities
- Product measures and Fubini–Tonelli
Measure and integration
Convergence theorems (MCT, Fatou, DCT)
Graduate analysis · Theoretical / proof-based
Topic
Convergence theorems (MCT, Fatou, DCT)
Graduate Analysis — scope drawn from Axler Measure, Integration & Real Analysis (open access), Bass Real Analysis for Graduate Students (free PDF), and typical first-year graduate analysis syllabi.