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)