rudin-real-complex-analysis

# Rudin's Real and Complex Analysis Reference skill for Walter Rudin's "Real and Complex Analysis" (3rd Edition) - a graduate-level text covering measure theory, integration, functional analysis, and complex analysis. ## When to Use Use this skill when working on: - Measure theory and Lebesgue integration - Lp spaces and functional analysis - Complex analysis (analytic functions, contour integration, residues) - Connections between real and complex analysis ## Topics Covered ### Real Analysis - Limits and continuity in metric spaces - Convergence of sequences and series - Differentiation and integration techniques - Metric spaces and topology ### Complex Analysis - Analytic functions and Cauchy-Riemann equations - Contour integration and Cauchy's theorem - Residue theorem and applications - Conformal mappings - Power series representations ### Topology - Topological spaces - Compactness and connectedness - Metric space topology ### Algebra - Rings and ideals (in context of function spaces) ## Decision Tree 1. **Measure/Integration Problem?** - Use Lebesgue dominated convergence - Check Fatou's lemma for liminf/limsup - Apply Fubini-Tonelli for iterated integrals 2. **Complex Analysis Problem?** - Check analyticity via Cauchy-Riemann - For integrals: residue theorem - For mappings: Schwarz lemma, conformal properties 3. **Functional Analysis?** - Riesz representation for duals - Hahn-Banach for extensions - Open mapping/closed graph theor...