The concept of measure is an extension of the concept of length: The measure of an interval in R is usually its length; the measure of a polygon in R 2 is usually its area; and so on. The problem of extending the classes of sets for which the notions of length, area, etc. are defined to larger classes of sets for which these notions are still defined gave rise to the general theory of measure.
KeywordsLebesgue Measure Finite Measure Outer Measure Lebesgue Measure Zero Pairwise Disjoint Interval
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