ABSTRACT
This chapter is a stepping stone for the subject of measure and integration. It defines the concept of an outer measure of a subset of the real line as a generalization of the concept of length of an interval, and then defines the concept of measure of certain subsets of the real line which must satisfy certain intuitively desirable properties. The properties of the class of subsets which can be measured is a motivation for the concept of a general measure in the context of an arbitrary set. The chapter outlines some properties of the Lebesgue outer measure. Although, the class of Lebesgue measurable sets is going to be very large, it is important to know that there are non-Lebesgue measurable sets. The Lebesgue outer measure of any interval is its length.
