1. Introduction to Measure Theory
MTH 426
Introduction to Measure Theory
By Dr. Saqib Hussain

2. MTH 426
Lecture # 14
Axiom of Choice

3. Previous Lecture’s Review

5. Theorem:
Ordinal multiplication is associative
Proof:

8. Choice Function:

9. Cartesian Product:

10. Axiom of choice:
Cartesian product of non empty family of non empty sets is non empty Or
There exists a choice function for any non empty family of non empty sets.

11. Axiom of choice:
Cartesian product of non empty family of non empty sets is non empty Or
There exists a choice function for any non empty family of non empty sets.

12. Zermelo’s Postulate:

13. Theorem:
Show that axiom of choice is equivalent to Zermelo’s postulate.
Proof: