In the context of Lebesgue measure, μ(a) represents the measure of a set 'a', which is a way to assign a numerical value to the size or extent of that set. This concept is central to understanding how Lebesgue measure quantifies subsets of Euclidean space, allowing for the integration and manipulation of functions defined over those sets. μ(a) is crucial for analyzing properties like completeness, translation invariance, and how it interacts with other mathematical constructs such as σ-algebras.
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