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| Real Analysis |
- Lebesgue Measure and Integral
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- Convergence theorems
- Differentiation of functions of bounded variation, differentiation of an indefinite integral, absolute continuity
- Holder and Minkowski inequalities, Lp spaces: completeness, representation of dual spaces
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- General Measure
- Signed measures, Radon-Nikodym theorem
- Outer measures, extension of a measure defined on an algebra or semialgebra
- Riesz representation theorem for positive linear functionals on C(X), dual space of C(X)
| References |
Folland: Real Anaylsis
Royden: Real Analysis
Rudin: Real and Complex Analysis
Rudin: Functional Analysis
Lang: Analysis
Reisz & Sz-Nagy: Functional Analysis
Dieudonne: Foundations of Modern Analysis
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