Abstract
This chapter discusses the Lebesgue measure of linear sets. It describes the conditions that need to be satisfied in the case of the Lebesgue measure: (1) it must always be nonnegative; (2) it must coincide with the measure for open sets defined; and (3) the measure of a countable number of disjoint measurable sets must be equal to the sum of their measures. The Lebesgue measure of a measurable set A is the greatest lower bound of the measures of its open supersets. The measure so defined is nonnegative. The union of sequence of measurable sets is a measurable set.
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