Wk  Lectures  Topics  Remarks 
1  9/16 
Review of the Riemann Integral
 
 9/18 
$\sigma$algebras and Borel sets
 
 9/20 
Measurable functions
 
2  9/23 
Simple functions
 
 9/25 
Measures
 
 9/27 
Integral of positive functions
 
3  9/30 
Integration of complex functions
 
 10/02 
Dominated Convergence, null sets
 
 10/04 
Outer measures
 Not in text 
4  10/07 
Outer measures continued and Lebesgue measure on the real line
 Not in text 
 10/09 
Lebesgue measure on the real line (Continued)
 Not in text 
 10/11 
Extension of premeasures
 Folland 
5  10/14 
Product measures
 Folland 
 10/16 
Integration on products
 Folland 
 10/17 
$L^1$spaces (xhour)
 
 10/18 
Complex and signed measures
 
6  10/21 
Modes of convergence
 
 10/23  Midterm exam

 10/25 
The RadonNikodym Theorem
 
7  10/28 
Holomorphic functions
 
 10/30 
Curves and paths
 
 11/01 
Integrals on paths
 
8  11/04 
Cauchy's Theorem for convex sets
 
 11/06 
Analyticity
 
 11/07 
Zeroes and singularities (xhour)
 
 11/08 
Cauchy estimates
 
9  11/11 
Local behavior of holomorphic functions
 
 11/13 
Chains, cycles, homology
 
 11/15 
Cauchy's Theorem, homotopy invariance
 
10  11/18 
Meromorphic functions, the Residue Theorem
 
 11/22  Final exam
