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The following notes have been taken as I studied for the quals as quick references for myself in the summer of 2010. It may be useful to a subset of you!

• Metric Space Topology
  • Ascoli-Arzelà
  • Stone-Weierstrass
  • Compactness
• Functions of a Real Variable
  • Riesz-Fischer
  • A non-measurable set
  • Signed measure: Hahn and Jordan decompositions
  • Radon-Nikodym
• Functions of a Complex Variable
  • Riemann Mapping Theorem