A measure on a set is a systematic way to assign to each suitable subset a number, intuitively interpreted as the size of the subset. In this sense, a measure is a generalization of the concepts of length, area, volume, etc. Measure theory is concerned with generalizing the notions of area on arbitrary sets of Euclidean spaces and notions of length of subsets of R. Essentially, it is a common ground for analysis of real functions and set theory.
A first course in measure theory will most likely devote time to many of the following topics:
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