Courses with significant overlap with this course:

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Course Contents

Algebras and s algebras, Measures, Outer measures, Lévesque measure in Rn, Completeness and regularity. Measurable functions and their properties, Convergence in measure, Integral, Convergence theorems. Signed and complex measures, Radon Nikodym theorem, Lévesque decomposition theorem, Lp spaces and their dual. Product measures, Construction, Fubini theorem and its applications, Differentiation of measures.