Lecture 05: Limits of sequences of sets and Monotone classes

In this lecture, we discuss the notions of increasing/decreasing sequences of sets and consider their limits. Using this notion, we discuss the concept of a Monotone class. For arbitrary sequences of sets, the notion of limit superior/inferior of the sequence is also introduced. Self-assessment / Activity questions: Given an increasing sequence of sets, is the union of the sets equal to the limit superior of the sequence? What is a Monotone class?