Measure Theory and Integrations Math 5820

References:
 1- P. M. Fitzpatrick and H. Royden, "Real Analysis," 4th edition, Pearson, 2010.
 2- J. Benedetto and W. Czaja, "Integration and Modern Analysis," Birkhauser, Boston, MA, 2009.
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Sets  and  Classes : Algebras, σ-algebras , Monotone classes.
 Measure and outer measure :   Measure,  Measurable sets , Outer measure , Extension of measure,  Completion, Lebesgue measure.
 Measurable functions :  Measure spaces,  Measurable functions,  Integrable   functions.
Convergence theorems and applications :  Fatou's lemma, Motonne convergence theorem, Dominated convergence  theorem, Differentiation and integration.
 Product spaces : Product measures and Fubini-Tonelli  theorem.

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