Chapter 6 - Constructing Measures

Question 1

Define a premeasure.

Define the outer measure induced by a premeasure mu.

Answer 1

Question 2

State Lemma 6.1 on four properties of the outer measure induced by mu.

Define an outer measure.

Answer 2

Question 3

Define a mu^*-measurable set.

State Lemma 6.2 on the relationship between algebra A and collection of mu^*-measurable sets.

Answer 3

Question 4

Define sigma-finite for premeasures.

State THM 6.2 - Hahn’s Extension Theorem.

Answer 4