MA 541 Analysis II – Study Guide
Test II will cover Sections 11.1-11.8, 10.1, and 10.2. There will be Definitions, Statements of Theorems, True-False questions, Proofs of theorems, Problem solving. The following table provides guidelines on what will be covered from each section.
|
Section |
Definitions |
State of Theorems |
Proofs |
|
11.1 |
Length of open and closed sets |
B |
C |
|
11.2 |
Inner and outer measure Measurable set |
F |
C |
|
11.3 |
A,B,E,F,G,H |
D,J |
|
|
11.4 |
Measurable functions |
D,E,F,G,H,I |
|
|
11.5 |
Measurable partition of [a,b] - B Upper and lower sums – C Lebesgue integral – F Lebesgue integrable function -F |
D |
I |
|
11.6 |
Lebesgue integral on measurable set - J |
A,B,C,D,F,G,K,N |
M |
|
11.7 |
Lebesgue integral for unbounded functions - B,E |
N |
|
|
11.8 |
A,B,D |
||
|
10.1 |
Uniform norm and uniform metric – A,C Normed space C[a,b] |
B,D,E |
|
|
10.2 |
Bernstein polynomials – D |
B,C,F |
D(6) |