Abstract
This chapter provides an overview of measure theory and discusses metric outer measure. If S is any space and μ* is any outer measure on S, then μ* has the additivity property expressed by μ*(A ∪ B ) = μ*A + μ*B provided A ∩ B = Ø and at least one of A or B is μ-measurable. The theorem that Lebesgue outer measure m* is a metric outer measure is proved. Various properties of lebesgue measure, and σ-algebras are discussed in the chapter. All Borel sets are Lebesgue measurable. The chapter also discusses Lebesgue outer k-measure, Fubini's theorem, outer ordinate sets, and Ergodic theory. Problems on inner measure, and outer measures from measures are also presented in the chapter.
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