Time:  MWF 3-4 pm

Location:  Altgeld Hall  347

Part I: Metric spaces
      1) R
      2) sequences  in R
      3) definition of metric spaces, open closed sets
      4) compact and complete sets
      5) continuous  functions
      6)  unique extension proinciple
      7)  Arzela-Ascoli
       8) Baire Category thm
       9) completion of metric spaces

Part II: Measurable sets and measures
      1) sigma-algebras, borel algebras
        2) measurses, probability measures
        3) outer measures and extension from algebras
        4) Lebesgue measure, Lusin's theorem
         5) Cantor set

H. L. Royden: Real Analysis, Prentive Hall

Remark: the notes in Part IV are based on P. Loeb's lecture notes for real analysis 2003

Homework (1/3-individual submission (always Mondays),
2 Midterm exams  (1/3)
Final exam  (1/3)

  Hw1

  Hw2

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