Lebesque Integral

Question 1

Give the standard representation

Answer 1

Question 2

What is the integral of a simple measurable function?

Answer 2

Question 3

Give properties of integrals of simple functions

Answer 3

Question 4

When is the integral of a simple measurable function finite

Answer 4

Question 5

What is the integral of a non negative function

Answer 5

Question 6

Give the properties of the integrals of non negative functions

Answer 6

Question 7

State the MCT

Answer 7

Question 8

State the corollary to the MCT

Answer 8

Question 9

State Fatou’s Lemma

Answer 9

Question 10

State Chebesyv Inequality

Answer 10

Question 11

When is an integral 0

Answer 11

Question 12

What does it mean for a function to be integrable

Answer 12

Question 13

State the DCT

Answer 13

Question 14

State the useful lemma when comparing the difference of simple measurable functions

Answer 14

Question 15

What is the relationship between continuity and riemann intergrability

Answer 15

Question 16

Define the Riemann integral

Answer 16

Question 17

Do lebesque and riemann agree

Answer 17

Question 18

Define the improper riemann integral

Answer 18

Question 19

Define the Riemann Stieljes Integral

Answer 19