Advanced Real Analysis

Course Description

This course covers Algebra of Sets, Relations and Functions, The Axion of Choice and Some Equivalents, Cardinal Numbers and Ordinal Numbers, Construction of the Real and Complex Number Fields, Topology and Continuous Functions, The Riemann-Stieltjes Intergral, Extending Certain Functionals, Measures and Measureable Sets, Measurable Functions, The Abstract Lebesque Integral, The Spaces Lp (1≤p<∞), Abstract Banach Spaces, The Conjugate Space of  Lp (1<p<∞), Abstract Hilbert Spaces, Differentiable and Non-Differentiable Functions, Absolutely continuous Functions, Complex Measure and the Lebesgue-Radon-Nikodym Theorem, Applications of the Lebesgue-Radon-Nikodym Theorem, The Product of Two Measure Spaces, Product of Infinitely Many Measure Spaces.


Basic Calculus and Algebra, Epsilon-Delta Language for Limits

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