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Measure Theory JohnK.Hunter

Measure TheoryJohn K. HunterDepartment of Mathematics, University of California at are some brief notes on Measure Theory , concentratingonLebesgue Measure onRn. Some missing topics I would have liked to have in-cluded had time permitted are: the change of variable formula for the Lebesgueintegral onRn; absolutely continuous functions and functions of boundedvari-ation of a single variable and their connection with Lebesgue-Stieltjes measuresonR; Radon measures onRn, and other locally compact Hausdorff topologicalspaces, and the Riesz representation theorem for bounded linear functionalson spaces of continuous functions; and other examples of measures, includingk-dimensional Hausdorff Measure inRn, Wiener Measure and Brownian mo-tion, and Haar Measure on topological groups.

Definition 1.5. A measurable space (X,A) is a non-empty set Xequipped with a σ-algebra A on X. It is useful to compare the definition of a σ-algebra with that of a topology in Definition 1.1. There are two significant differences. First, the complement of a measurable set is measurable, but the complement of an open set is not, in general,

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