Math Notes

Math 564: Real Analysis and Measure Theory

Fall 2025

Topics: measures, their construction and properties, Borel-Cantelli lemmas, regularity, tightness, measurable functions and integration, modes of convergence, Fubini-Tonelli, signed measures, Radon-Nikodym derivatives, Lebesgue density, a.e. differentiability, and examples from ergodic theory.