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What is Lebesgue Measure and Outer Measure about?

This chapter introduces Lebesgue measure and the Cantor set. It develops Lebesgue measure on the real line by approximating sets with countable unions of intervals. The measure of a set is defined as the infimum of the lengths of covering intervals. Lebesgue measure generalizes the notion of length and the measure of an interval is equal to its length. The chapter also defines the Cantor set through a recursive process of removing middle thirds and shows it is an uncountable set with measure zero.

Author

Ana-Maria V Ciobanu

Language

EN